SUB-PLACEMENT AGENT AGREEMENT Franklin Distributors, LLC One Franklin Parkway San Mateo, CA 94403

Exhibit (h)(2)

SUB-PLACEMENT AGENT AGREEMENT

Franklin Distributors, LLC

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San Mateo, CA 94403

July 21, 2025

UBS Securities LLC

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New York, New York 10019

RE: At-the-Market Offerings by Western Asset Municipal High Income Fund Inc.

Ladies and Gentlemen:

From time to time ▇▇▇▇▇▇▇▇ Distributors, LLC (in such capacity, together with its affiliates, the “Distributor,” “we” or “us”) will act as manager of registered at-the-market offerings by Western Asset Municipal High Income Fund Inc., a Maryland corporation (the “Fund”), of up to $75,000,000 of shares (the “Shares”) of common stock, $0.01 par value per share, of the Fund (the “Common Shares”). In the case of such offerings, the Fund has agreed with the Distributor to issue and sell through the Distributor, as sales agent, the Shares (the “Distribution Agreement”).

We hereby agree to retain UBS Securities LLC (the “Agent” or “you”) as a sub-placement agent with respect to the offerings of the Shares to be issued and sold by the Fund (the “Offerings”) as the Fund and the Distributor may indicate from time to time, and you agree to act in such capacity, all upon, and subject to, the terms and conditions set forth below:

SECTION 1. Description of Offerings.

(a) The Shares are to be sold on a daily basis or otherwise as shall be agreed to by the Fund together with Agent or the Distributor on any day (each, an “Offering Date”) that is a trading day for the exchange on which the Shares are listed and primarily trade (the “Stock Exchange”) (other than a day on which the Stock Exchange is scheduled to close prior to its regular weekday closing time). Promptly after the Fund and the Distributor have determined the maximum amount of the Shares to be distributed by the Distributor for any Offering Date, which shall not in any event exceed the amount available for issuance under the currently effective Registration Statement (as defined herein) (the “Maximum Daily Amount”), and the Minimum Daily Price (as defined herein), the Distributor shall advise the Agent of the Maximum Daily Amount and the Minimum Daily Price. Subject to the terms and conditions herein, the Agent shall use its reasonable best efforts to sell all of the Shares designated in accordance with the plan of distribution set forth in the Prospectus Supplement (as defined herein); provided, however, that in no event shall the Agent sell Shares in excess of the Maximum Daily Amount or for a price per Share below the Minimum Daily Price. The gross sales price of the Shares sold under this Section 1(a) shall be the market price at which the Agent sells such Shares. The “Minimum Daily Price” means the minimum price per Share below which the Shares may not be sold by the Agent on any Offering Date, which shall not in any event be less than the current net

asset value of such Shares (which net asset value shall be determined as of a time within twenty-four (24) hours, excluding Saturdays, Sundays and holidays, next preceding the time of such determination), plus the per Share amount of the commission to be paid to the Distributor.

(b) Notwithstanding the foregoing, the Distributor or the Fund may instruct the Agent by telephone (confirmed promptly by e-mail or other electronic means) of a revised Minimum Daily Price and/or a revised Maximum Daily Amount and the Agent shall not sell Shares for a price per Share below such revised Minimum Daily Price, or in a quantity in excess of such revised Maximum Daily Amount, after the giving of such notice. In addition, the Fund, or the Distributor in consultation with the Fund, may, upon notice to the Agent by telephone (confirmed promptly by e-mail or other electronic means), suspend the offering of the Shares at any time; provided, however, that such suspension or termination shall not affect or impair the parties’ respective obligations with respect to the Shares sold hereunder prior to the giving of such notice.

(c) The Agent agrees not to make any sales of the Shares pursuant to this Section 1, other than through transactions for which compliance with Rule 153 under the Securities Act of 1933, as amended, and the rules and regulations thereunder (collectively, the “Securities Act”), will satisfy the prospectus delivery requirements of Section 5(b)(2) of the Securities Act.

(d) The compensation to the Agent, as a sub-placement agent for each sale of the Shares pursuant to this Section 1, shall be the Applicable Selling Agent Commission (as set forth on the Addendum hereto) with respect to the Shares sold, multiplied by the Gross Sales Proceeds (the “Agent Compensation”), as further described in the Addendum to this Sub-Placement Agent Agreement (the “Agreement”). The Agent shall not be responsible for any fees imposed by any governmental or self-regulatory organization on the Fund or the Distributor in respect of such sales. The Distributor may pay the Agent Compensation to the Agent, or may authorize the Agent to retain the Agent Compensation from the Gross Sales Proceeds. The Agent Compensation shall be payable solely out of the compensation the Distributor receives from the Fund pursuant to the Distribution Agreement (the “Related Compensation”). Notwithstanding anything to the contrary in any other provision of this Agreement (or, for the avoidance of doubt, in the Addendum hereto), the Distributor shall have no obligation to pay any portion of the Agent Compensation to the Agent, or authorize the retention by the Agent of any portion of the Agent Compensation from the Gross Sales Proceeds, until the Distributor receives at least an equivalent amount of Related Compensation, and the Distributor’s obligation to the Agent for the Agent Compensation is limited solely to amounts payable out of the Related Compensation.

(e) The Agent shall provide written confirmation to the Distributor following the close of trading on the Stock Exchange on each Offering Date setting forth for each sale the number of Shares sold, the time of sale, the Gross Sales Price (as defined in the Addendum to this Agreement) per Share, and the compensation that the Agent is owed with respect to such sales.

(f) Settlement for sales of the Shares pursuant to this Section 1 will occur on the business day following the date on which such sales are made (each such day, a “Settlement Date”), unless otherwise agreed in accordance with the Distribution Agreement. On each Settlement Date, the Shares sold through the Agent for settlement on such date shall be delivered by the Fund at the request of the Distributor to the Agent against payment of (i) the Gross Sales Proceeds for the sale of such Shares or (ii) to the extent authorized by the Distributor, the Gross

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Sales Proceeds, less the Related Compensation. If the Agent is authorized by the Distributor to retain the Agent Compensation from the Gross Sales Proceeds for the sale of the Shares, then the Agent shall (i) pay to the Distributor an amount equal to the Related Compensation minus the Agent Compensation in same day funds delivered to the account(s) designated by the Distributor and (ii) remit to the Fund the Gross Sales Proceeds, less the Related Compensation. If the Distributor shall default on its obligation to deliver the Shares on any Settlement Date, subject to the terms of Section 5 herein, the Distributor shall (A) hold the Agent harmless against any reasonable loss, claim or damage arising from or as a result of such default by the Distributor and (B) pay the Agent any commission to which it would otherwise be entitled absent such default. If the Agent breaches this Agreement by failing to deliver proceeds on any Settlement Date for the Shares delivered by the Distributor, subject to the terms of Section 5 herein, the Agent shall (A) hold the Distributor harmless against any reasonable loss, claim or damage arising from or as a result of such default by the Agent, (B) deliver such proceeds to the Distributor as soon as practicable and (C) pay the Distributor interest based on the effective overnight Federal Funds rate.

(g) In connection with this Agreement and the Offerings, the Distributor shall, no more than once per calendar quarter in which the Fund and the Distributor have requested, or anticipate requesting, that the Agent sell Shares pursuant to an Offering, provide to the Agent such certificates and other documents, in any case, as the Agent may reasonably request upon reasonable notice (but in no event upon notice of less than five business days) relating to authorization, capacity, enforceability and compliance matters. Any such certifications shall be made as of the end of the calendar quarter immediately preceding the calendar quarter in which such request by the Agent is made.

(h) In connection with this Agreement and the Offerings, the Agent will promptly notify the Fund and the Distributor of any material non-confidential claim or complaint, any material enforcement action or other material proceeding by a regulatory authority with respect to the Fund, the Shares or the Offerings against or directed at or to the Agent or its principals, affiliates, officers, directors, employees or agents, or any person who controls the Agent, within the meaning of Section 15 of the Securities Act.

(i) In connection with this Agreement and the Offerings, the Agent will promptly notify the Fund and the Distributor of any examination by any regulatory agency or self-regulatory organization that has resulted in a material compliance deficiency in connection with the Offerings.

(j) The Agent shall timely file with the Financial Industry Regulatory Authority, Inc. (“FINRA”) all sales literature and other filings that may be required in connection with the Offerings.

SECTION 2. Representations and Warranties by the Distributor. The Distributor represents, warrants to and agrees with the Agent, as of the date hereof and as of each Offering Date and Settlement Date, that:

(a) Based upon the representations made by the Fund to the Distributor in the Distribution Agreement, a registration statement on Form N-2 (File No. 333-287133 and 811-05497)

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(the “Registration Statement”) (i) has been prepared by the Fund in conformity with the requirements of the Securities Act and the Investment Company Act of 1940, as amended, and the rules and regulations thereunder (collectively, the “1940 Act”) in all material respects; (ii) has been filed with the U.S. Securities and Exchange Commission (the “Commission”) under the Securities Act and the 1940 Act; and (iii) heretofore became, and is, effective; the Registration Statement sets forth the terms of the offering, sale and plan of distribution of the Shares and contains additional information concerning the Fund and its business; no stop order of the Commission preventing or suspending the use of the Basic Prospectus (as defined herein), the Prospectus Supplement (as defined herein) or the Prospectus (as defined herein), or the effectiveness of the Registration Statement, has been issued, and no proceedings for such purpose have been instituted or, to the Fund’s knowledge, have been threatened by the Commission. Except where the context otherwise requires, “Registration Statement,” as used herein, means, collectively, the various parts of the Registration Statement pertaining to the offering and sale of the Shares, as amended at the time of effectiveness for purposes of Section 11 of the Securities Act (the “Effective Time”), as such section applies to the Distributor, including (1) all documents filed as a part thereof or incorporated or deemed to be incorporated by reference therein and (2) any information contained or incorporated by reference in a prospectus filed with the Commission pursuant to Rule 424(b) under the Securities Act, to the extent such information is deemed, pursuant to Rule 430B or Rule 430C under the Securities Act, to be part of the Registration Statement at the Effective Time. “Basic Prospectus,” as used herein, means the final prospectus filed as part of the Registration Statement, including the related statement of additional information, together with any amendments or supplements thereto as of the date of this Agreement. Except where the context otherwise requires, “Prospectus Supplement,” as used herein, means the final prospectus supplement, including the related statement of additional information, relating to the Shares, filed by the Fund with the Commission pursuant to Rule 424(b) under the Securities Act, in the form furnished by the Fund to the Distributor in connection with the offering of the Shares. Except where the context otherwise requires, “Prospectus,” as used herein, means the Prospectus Supplement together with the Basic Prospectus attached to or used with the Prospectus Supplement. Any reference herein to the Registration Statement, the Basic Prospectus, the Prospectus Supplement or the Prospectus shall be deemed to refer to and include the documents, if any, incorporated by reference, or deemed to be incorporated by reference, therein.

(b) Based upon the representations made by the Fund to the Distributor in the Distribution Agreement, (i) the Fund is duly registered under the 1940 Act as a closed-end management investment company; (ii) a notification of registration of the Fund as an investment company under the 1940 Act on Form N-8A (the “1940 Act Notification”) has been prepared by the Fund in conformity with the 1940 Act and has been filed with the Commission and, at the time of filing thereof and at the time of filing any amendment or supplement thereto, conformed in all material respects with all applicable provisions of the 1940 Act; (iii) the Fund has not received any notice in writing from the Commission pursuant to Section 8(e) of the 1940 Act with respect to the 1940 Act Notification or the Registration Statement (or any amendment or supplement to either of them); and (iv) no person is serving or acting as an officer, director or investment adviser of the Fund except in accordance with the provisions of the 1940 Act, provided that for purposes of the foregoing representation with respect to officers and directors of the Fund, the Fund shall be entitled to rely on representations from such officers and directors.

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(c) Based upon the representations made by the Fund to the Distributor in the Distribution Agreement, the Registration Statement, the 1940 Act Notification and the Prospectus, as from time to time amended or supplemented, each complied when it became effective or was filed (as the case may be), complies as of the date hereof and, as amended or supplemented, will comply, at each time of purchase of Shares in connection with each Offering, and at all times during which a prospectus is required by the Securities Act to be delivered in connection with any sale of Shares, in all material respects, with the requirements of the Securities Act and the 1940 Act; the Registration Statement did not, as of the Effective Time, contain an untrue statement of a material fact or omit to state a material fact required to be stated therein or necessary to make the statements therein not misleading; at no time during the period that begins on the earlier of the date of the Basic Prospectus or the date the Basic Prospectus was filed with the Commission and ends at the later of each time of purchase of Shares in connection with each Offering or the end of the period during which a prospectus is required by the Securities Act to be delivered in connection with any sale of Shares, did or will the Prospectus, as from time to time amended or supplemented, include an untrue statement of a material fact or omit to state a material fact necessary in order to make the statements therein, in the light of the circumstances under which they were made, not misleading; provided, however, that the Distributor does not make any representation or warranty with respect to any statement contained in the Registration Statement, the Basic Prospectus or the Prospectus in reliance upon and in conformity with information furnished in writing by the Agent or on the Agent’s behalf to the Distributor or the Fund expressly for use in the Registration Statement or the Prospectus (the “Agent Provided Information”). The Agent confirms that (i) the Agent’s name on the front cover and under the headings “Prospectus Supplement Summary – The Offering” and “Plan of Distribution” in the Prospectus Supplement and (ii) the tenth paragraph and the second sentence in the eleventh paragraph under the heading “Plan of Distribution” in the Prospectus Supplement was the only information furnished in writing to the Distributor or the Fund by or on behalf of the Agent expressly for use in the Registration Statement or Prospectus.

(d) Based upon the representations made by the Fund to the Distributor in the Distribution Agreement, the financial statements incorporated by reference in the Registration Statement or the Prospectus, together with the related notes and schedules, (i) present fairly in all materials respects the financial position of the Fund as of the dates indicated and the results of operations, cash flows and changes in shareholders’ equity of the Fund for the periods specified and (ii) have been prepared in compliance in all material respects with the requirements of the Securities Act, the 1940 Act and the Securities Exchange Act of 1934, as amended, and the rules and regulations thereunder (collectively, the “Exchange Act”), and in conformity in all material respects with U.S. generally accepted accounting principles applied on a consistent basis during the periods involved; the other financial and statistical data contained or incorporated by reference in the Registration Statement or the Prospectus are accurately and fairly presented, in all material respects, and prepared on a basis consistent with the financial statements and books and records of the Fund in all material respects; there are no financial statements that are required to be included or incorporated by reference in the Registration Statement, the Basic Prospectus or the Prospectus by the Securities Act, the 1940 Act or the Exchange Act that are not included or incorporated by reference as required; and the Fund does not have any material liabilities or obligations, direct or contingent (including any off-balance sheet obligations), not described in the Registration Statement (excluding the exhibits thereto).

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(e) Based upon the representations made by the Fund to the Distributor in the Distribution Agreement, as of the date of this Agreement, the Fund has an authorized and outstanding capitalization as set forth in the Registration Statement, the Basic Prospectus and the Prospectus and, with respect to any issuance and sale under this Agreement, the Fund shall have as of the date of the most recent amendment or supplement to the Registration Statement or Prospectus, an authorized and outstanding capitalization as set forth in the Registration Statement and the Prospectus; all of the issued and outstanding Common Shares have been duly authorized and validly issued and are fully paid and non-assessable, have been issued in material compliance with all applicable securities laws and were not issued in violation of any preemptive right, resale right, right of first refusal or similar right.

(f) Based upon the representations made by the Fund to the Distributor in the Distribution Agreement, (i) the Fund has been duly formed, is validly existing and is in good standing as a Maryland corporation under the laws of Maryland, with full power and authority to own, lease and operate and conduct its business as described in the Registration Statement, the Basic Prospectus and the Prospectus and to issue, sell and deliver the Shares as contemplated herein; and (ii) the Fund is duly qualified to do business as a foreign entity and is in good standing in each jurisdiction where the conduct of its business requires such qualification, except where the failure to be so qualified and in good standing would not, individually or in the aggregate, have a material adverse effect on the business, properties, financial condition or results of operations of the Fund.

(g) Based upon the representations made by the Fund to the Distributor in the Distribution Agreement, (i) the Shares have been duly and validly authorized and, when issued and delivered against payment therefor as provided herein, will be duly and validly issued, fully paid and non-assessable and free of statutory and contractual preemptive rights, resale rights, rights of first refusal and similar rights; (ii) the Shares, when issued and delivered against payment therefor as provided herein, will be free of any restriction upon the voting or transfer thereof pursuant to the Fund’s Articles of Incorporation, as amended or supplemented, the Fund’s Fourth Amended and Restated Bylaws, as further amended or supplemented, or any agreement or other instrument to which the Fund is a party; (iii) the Common Shares, including the Shares, conform in all material respects to the description thereof, if any, contained or incorporated by reference in the Registration Statement, the Basic Prospectus or the Prospectus; (iv) the certificates for the Shares, if any, are in due and proper form; (v) the Fund is in material compliance with the rules of the Stock Exchange, including, without limitation, the requirements for continued listing of the Common Shares on the Stock Exchange and the Fund has not received any written notice from the Stock Exchange regarding the delisting of the Common Shares from the Stock Exchange; and (vi) the Shares will be duly listed, and admitted and authorized for trading, subject to official notice of issuance, on the Stock Exchange.

(h) The Distributor has full corporate power and authority to enter into this Agreement and the transactions contemplated hereby. This Agreement has been duly authorized, executed and delivered by the Distributor. Assuming due authorization, execution and delivery of this Agreement by the Agent, this Agreement constitutes a valid and binding agreement of the Distributor and is enforceable against the Distributor in accordance with its terms, except as the enforceability hereof and thereof may be limited by applicable bankruptcy, insolvency, reorganization and similar laws affecting creditors’ rights generally and moratorium laws in effect from time to time and by equitable principles restricting the availability of equitable remedies.

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(i) Based upon the representations made by the Fund to the Distributor in the Distribution Agreement, no approval, authorization, consent or order of or filing with any federal, state, local or foreign governmental or regulatory commission, board, body, authority or agency, or of or with any self-regulatory organization or other non-governmental regulatory authority (including, without limitation, the Stock Exchange), or approval of the shareholders of the Fund that has not already been obtained, is required in connection with the issuance and sale of the Shares or the consummation by the Fund of the transactions contemplated hereby, other than (i) the registration of the Shares under the Securities Act, which has been effected, (ii) the listing of the Shares with the Stock Exchange, upon official notice of issuance, (iii) any necessary qualification under the securities or blue sky laws of the various jurisdictions in which the Shares are being offered through the Agent or (iv) any necessary qualification pursuant to the rules of FINRA.

SECTION 3. Representations and Warranties by the Agent. The Agent represents, warrants to and agrees with the Distributor, as of the date hereof and as of each Offering Date and Settlement Date, that:

(a) The Agent has full corporate power and authority to enter into this Agreement and the transactions contemplated hereby. This Agreement has been duly authorized, executed and delivered by the Agent. Assuming due authorization, execution and delivery by the Distributor, this Agreement constitutes a valid and binding agreement of the Agent and is enforceable against the Agent in accordance with its terms, except as the enforceability hereof and thereof may be limited by applicable bankruptcy, insolvency, reorganization and similar laws affecting creditors’ rights generally and moratorium laws in effect from time to time and by equitable principles restricting the availability of equitable remedies.

(b) The Agent Provided Information is or will be complete and accurate in all material respects and does not or will not, as from time to time amended or supplemented, include an untrue statement of a material fact or omit to state a material fact required to be stated therein or necessary in order to make the statements therein, in the light of the circumstances under which they were made, not misleading.

(c) The Agent has adopted and implemented written policies and procedures reasonably designed to prevent violation of federal and state securities laws, including policies and procedures that provide oversight of compliance by each registered representative of the Agent.

SECTION 4. Additional Covenants.

(a) The Agent ▇▇▇▇▇▇ confirms that it is actually engaged in the investment banking and securities business and is a member in good standing with FINRA and hereby agrees that it will undertake to comply with all applicable FINRA rules (as amended from time to time, including without limitation, any successor provision) in connection with acting as sub-placement agent for the sale of the Shares. The Agent further agrees that in acting as sub-placement agent for the sale of the Shares, it will comply with all applicable laws, rules and regulations, including the

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applicable provisions of the Securities Act, the Exchange Act, and the 1940 Act, and the applicable rules and regulations of the Commission thereunder, and the applicable rules and regulations of any state or any securities exchange or self-regulatory organization having jurisdiction over the relevant Offering.

(b) The Agent ▇▇▇▇▇▇ agrees that in acting as sub-placement agent for the sale of the Shares, it will not use, authorize use of, refer to, or participate in the planning for use of any “written communication” (as defined in Rule 405 under the Securities Act) concerning any Offering, other than the Prospectus. The Agent further agrees that in acting as sub-placement agent for the sale of the Shares, it is not authorized by the Distributor or the Fund or any other seller of the Shares offered pursuant to the Prospectus to give any information or to make any representation not contained in the Prospectus in connection with the sale of such Shares.

(c) The Distributor shall not be under any obligation to the Agent except for obligations assumed hereunder or in writing by the Distributor in connection with any Offering. Nothing contained herein or in any communication in writing from us shall constitute the Distributor and the Agent an association or partners with one another. If such parties should be deemed to constitute a partnership for Federal income tax purposes, then the Agent elects to be excluded from the application of Subchapter K, Chapter 1, Subtitle A of the Internal Revenue Code of 1986, as amended, and agrees not to take any position inconsistent with that election. The Agent authorizes the Distributor, in its discretion, to execute and file on its behalf such evidence of that election as may be required by the Internal Revenue Service. In connection with any Offering, each party shall be liable for its proportionate amount of any tax, claim, demand or liability that may be asserted against it alone, based upon the claim that either of them constitutes an association, an unincorporated business or other entity, including, in each case, its proportionate amount of any expense incurred in defending against any such tax, claim, demand or liability.

(d) The parties acknowledge and agree that all share-related numbers contained in this Agreement shall be adjusted to take into account any stock split effected with respect to the Shares.

(e) The Agent shall at all times comply with the offering requirements as set forth herein and under the heading “Plan of Distribution” in the Prospectus.

(f) The Agent will limit its interest in any Offering solely to the Applicable Selling Agent Commission, which shall not exceed the usual and customary distributor’s or selling agent’s commission in the Offerings.

(g) The Agent has not and will not, acting alone or in concert with others, initiate or direct the formation of an underwriting syndicate in any Offering.

SECTION 5. Indemnification and Contribution.

(a) The Distributor agrees to indemnify, defend and hold harmless the Agent, its partners, directors and officers, and any person who controls the Agent within the meaning of Section 15 of the Securities Act or Section 20 of the Exchange Act, and the successors and assigns of all of the foregoing persons, from and against any reasonable loss, damage, expense, liability or claim (including the reasonable cost of investigation) which the Agent or any such

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person may incur under the Securities Act, the 1940 Act, the Exchange Act, the common law or otherwise, insofar as such loss, damage, expense, liability or claim (or any actions or proceedings in respect thereof) arises out of or is based upon (i) any material breach of any representation, warranty, covenant or agreement of the Distributor contained in this Agreement, (ii) any material violation by the Distributor of any law, rule or regulation (including any rule of any self-regulatory organization) applicable to the Offerings, or (iii) any untrue statement or alleged untrue statement of a material fact appearing in the Registration Statement or Prospectus or omission or alleged omission to state a material fact required to be stated therein or necessary to make the statements therein, in the light of the circumstances in which they were made, not misleading, except to the extent such statements were included in the Registration Statement or Prospectus in reliance upon and in conformity with the Agent Provided Information.

(b) The Agent agrees to indemnify, defend and hold harmless the Distributor, the Fund, their partners, directors and officers, and any person who controls the Distributor or the Fund within the meaning of Section 15 of the Securities Act or Section 20 of the Exchange Act, and the successors and assigns of all of the foregoing persons, from and against any loss, damage, expense, liability or claim (including the reasonable cost of investigation) which the Distributor, the Fund or any such other person may incur under the Securities Act, the 1940 Act, the Exchange Act, the common law or otherwise, insofar as such loss, damage, expense, liability or claim (or any actions or proceedings in respect thereof) arises out of or is based upon (i) any material breach of any representation, warranty, covenant or agreement of the Agent contained in this Agreement or (ii) any material violation by the Agent of any law, rule or regulation (including any rule of any self-regulatory organization), or (iii) any untrue statement or alleged untrue statement or omission or alleged omission made in the Registration Statement or the Prospectus in reliance upon and in conformity with the Agent Provided Information.

(c) An indemnified person under Section 5 of this Agreement (the “Indemnified Party”) shall give written notice to the other party (the “Indemnifying Party”) of any loss, damage, expense, liability or claim in respect of which the Indemnifying Party has a duty to indemnify such Indemnified Party under Section 5(a) or (b) of this Agreement (a “Claim”), specifying in reasonable detail the nature of the loss, damage, expense, liability or claim for which indemnification is sought, except that any delay or failure so to notify such Indemnifying Party shall only relieve such Indemnifying Party of its obligations hereunder to the extent, if at all, that such Indemnifying Party is actually prejudiced by reason of such delay or failure.

(d) If a Claim results from any action, suit or proceeding brought or asserted against an Indemnified Party, the Indemnifying Party shall assume the defense thereof, including the employment of counsel reasonably satisfactory to the Indemnified Party and the payment of all fees and expenses. The Indemnified Party shall have the right to employ separate counsel in such action, suit or proceeding and participate in such defense thereof, but the fees and expenses of such separate counsel shall be at the expense of the Indemnified Party unless (i) the Indemnifying Party has agreed in writing to pay such fees and expenses, (ii) the Indemnifying Party has failed within a reasonable time to assume the defense and employ counsel or (iii) the named parties to any such action, suit or proceeding (including any impleaded parties) include both such Indemnified Party and Indemnifying Party and such Indemnified Party shall have been advised by its counsel that representation of such Indemnified Party and Indemnifying Party by the same counsel would be inappropriate under applicable standards of professional conduct

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(whether or not such representation by the same counsel has been proposed) due to actual or potential differing interests between the Indemnifying Party and the Indemnified Party (in which case the Indemnifying Party shall not have the right to assume the defense of such action, suit or proceeding on behalf of such Indemnified Party). It is understood, however, that the Indemnifying Party shall, in connection with any one action, suit or proceeding or separate but substantially similar or related actions, suits or proceedings in the same jurisdiction arising out of the same general allegations or circumstances be liable for the reasonable fees and expenses of only one separate firm of attorneys (in addition to any local counsel) at any time for all such Indemnified Parties not having actual or potential differing interests with the Indemnifying Party or among themselves, which firm shall be designated in writing by an authorized representative of such parties and that all such fees and expenses shall be reimbursed promptly as they are incurred. The Indemnifying Party shall not be liable for any settlement of any such action, suit or proceeding effected without its written consent, but if settled with such written consent or if there be a final judgment for the plaintiff in any such action, suit or proceeding, the Indemnifying Party agrees to indemnify and hold harmless any Indemnified Party from and against any loss, liability, damage or expense by reason by such settlement or judgment.

(e) With respect to any Claim not within Paragraph (d) of Section 5 hereof, the Indemnifying Party shall have 20 days from receipt of notice from the Indemnified Party of such Claim within which to respond thereto. If the Indemnifying Party does not respond within such twenty-day period, it shall be deemed to have accepted responsibility to make payment and shall have no further right to contest the validity of such Claim. If the Indemnifying Party notifies the Indemnified Party within such twenty-day period that it rejects such Claim in whole or in part, the Indemnified Party shall be free to pursue such remedies as may be available to the Indemnified Party under applicable law.

(f) If the indemnification provided for in this Section 5 is unavailable to an Indemnified Party or insufficient to hold an Indemnified Party harmless in respect of any losses, damages, expenses, liabilities or claims referred to therein, then each applicable Indemnifying Party shall contribute to the amount paid or payable by such Indemnified Party as a result of such losses, damages, expenses, liabilities or claims in such proportion as is appropriate to reflect (i) the relative benefits received by the Indemnified Party, on the one hand, and the Indemnifying Party, on the other hand, from the offering of the Shares; or (ii) if, but only if, the allocation provided for in clause (i) is not permitted by applicable law, in such proportion as is appropriate to reflect not only the relative benefits referred to in clause (i) but also the relative fault of the Indemnified Party, on the one hand, and of the Indemnifying Party, on the other, in connection with any statements or omissions or other matters which resulted in such losses, damages, expenses, liabilities or claims, as well as any other relevant equitable considerations. The relative benefits received by the Distributor, on the one hand, and the Agent, on the other, shall be deemed to be in the same respective proportions as the total compensation received by the Distributor from sales of the Shares bears to the total compensation received by the Agent from sales of the Shares. The relative fault of the parties hereto shall be determined by reference to, among other things, whether the untrue statement or alleged untrue statement of a material fact or omission or alleged omission relates to information supplied by such party, on one hand, or by the other party, on the other hand, and the parties’ relative intent, knowledge, access to information and opportunity to correct or prevent such statement or omission. The amount paid or payable by a party hereto as a result of the losses, damages, expenses, liabilities and claims referred to in this

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subsection shall be deemed to include any legal or other fees or expenses reasonably incurred by such party in connection with investigating, preparing to defend or defending any proceeding. The parties hereto agree that it would not be just and equitable if contribution pursuant to this Section 5 were determined by pro rata allocation or by any other method of allocation that does not take account of the equitable considerations referred to in this subsection (f). No person guilty of fraudulent misrepresentation (within the meaning of Section 11(f) of the Securities Act) shall be entitled to contribution from any person who was not guilty of such fraudulent misrepresentation. Notwithstanding the foregoing provisions of this subsection (f), the Agent shall not be required to contribute any amount in excess of the commissions received by it under this Agreement.

(g) The indemnity and contribution agreements contained in this Section 5 and the covenants, warranties and representations of the parties contained in this Agreement shall remain in full force and effect regardless of any investigation made by or on behalf of the Agent, its partners, directors or officers or any person (including each partner, officer or director of such person) who controls the Agent within the meaning of Section 15 of the Securities Act or Section 20 of the Exchange Act, or by or on behalf of the Distributor, its directors or officers or any person who controls the Distributor within the meaning of Section 15 of the Securities Act or Section 20 of the Exchange Act, and shall survive any termination of this Agreement or the issuance and delivery of the Shares.

(h) IN NO EVENT WILL ANY PARTY TO THIS AGREEMENT BE LIABLE TO ANY OTHER PERSON OR ANY THIRD PARTY FOR ANY CONSEQUENTIAL, INCIDENTAL, SPECIAL OR INDIRECT DAMAGES (INCLUDING BUT NOT LIMITED TO LOST PROFITS), EVEN IF SUCH PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH LOSSES.

SECTION 6. Termination.

(a) This Agreement shall continue in full force and effect until terminated by either party, including by written instruction by the Fund to the Distributor, by five (5) days’ written notice to the other party; provided that if this Agreement has become effective with respect to any Offering pursuant to this Agreement, this Agreement may not be terminated by either party with respect to such Offering; provided further that this Agreement shall terminate automatically upon termination of the Distribution Agreement.

(b) This Agreement shall remain in full force and effect unless terminated pursuant to Section 6(a) hereof or otherwise by mutual agreement of the parties; provided that any such termination by mutual agreement shall in all cases be deemed to provide that Section 5 shall remain in full force and effect.

(c) Any termination of this Agreement shall be effective on the date specified in such notice of termination; provided that in any event such termination shall not be effective until any earlier than the close of business on the fifth day after receipt of such notice by the Distributor or the Agent, as the case may be. If such termination shall occur prior to the Settlement Date for any sale of the Shares, such sale shall settle in accordance with the provisions of Section 1 of this Agreement.

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SECTION 7. Notices. Except as otherwise herein provided, all statements, requests, notices and agreements under this Agreement shall be in writing and delivered by hand, overnight courier, mail or email and shall be sufficient in all respects if delivered or sent to:

If to the Distributor:

Franklin Distributors, LLC

▇▇▇ ▇▇▇▇▇ ▇▇▇▇▇▇▇▇ ▇▇▇▇▇

Stamford, CT 06902

Attn: Legal Department

Email: ▇▇▇▇.▇▇▇▇▇▇▇▇▇▇@▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇.▇▇▇

If to the Agent:

UBS Securities LLC

▇▇▇▇ ▇▇▇▇▇▇ ▇▇ ▇▇▇ ▇▇▇▇▇▇▇▇

New York, New York 10019

Attn: ▇▇▇▇▇▇ ▇▇▇▇▇▇▇▇

Email: ▇▇▇▇▇▇.▇▇▇▇▇▇▇▇@▇▇▇.▇▇▇

Each party to this Agreement may change such address for notices by sending to the parties to this Agreement written notice of a new address for such purpose.

SECTION 8. Parties in Interest. The Agreement herein set forth has been and is made solely for the benefit of the Distributor, the Fund and the Agent and, to the extent provided in Section 5 of this Agreement, the partners, directors, officers and controlling persons (within the meaning of Section 15 of the Securities Act or Section 20 of the Exchange Act) referred to in such section, and their respective successors and assigns. No other person, partnership, association or corporation (including a purchaser, as such purchaser, from the Distributor) shall acquire or have any right under or by virtue of this Agreement.

SECTION 9. No Fiduciary Relationship. The Distributor hereby acknowledges that the Agent is acting solely as sub-placement agent in connection with the sale of the Shares and that the Agent is acting pursuant to a contractual relationship created solely by this Agreement entered into on an arm’s length basis, and in no event do the parties intend that the Agent act or be responsible as a fiduciary to the Distributor or the Fund, their respective management, shareholders or creditors, or any other person in connection with any activity that the Agent may undertake or have undertaken in furtherance of the sale of the Shares, either before or after the date hereof.

SECTION 10. Entire Agreement. This Agreement constitutes the entire agreement and supersedes all other prior and contemporaneous agreements and undertakings, both written and oral, among the parties hereto with regard to the subject matter hereof.

SECTION 11. Counterparts; Heading. This Agreement may be signed by the parties in one or more counterparts which together shall constitute one and the same agreement among the parties. The Section headings in this Agreement have been inserted as a matter of convenience of reference and are not a part of this Agreement.

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SECTION 12. Law; Construction. This Agreement and any claim, counterclaim or dispute of any kind or nature whatsoever arising out of or in any way relating to this Agreement (“Dispute”), directly or indirectly, shall be governed by, and construed in accordance with, the internal laws of the State of New York.

SECTION 13. Submission to Jurisdiction. Except as set forth below, no Dispute may be commenced, prosecuted or continued in any court other than the courts of the State of New York located in the City and County of New York or in the United States District Court for the Southern District of New York, which courts shall have jurisdiction over the adjudication of such matters, and each party hereto consents to the jurisdiction of such courts and personal service with respect thereto. Each party hereto hereby consents to personal jurisdiction, service and venue in any court in which any Dispute arising out of or in any way relating to this Agreement is brought by any third party against any Indemnified Party. Each party hereto (on its behalf and, to the extent permitted by applicable law, on behalf of its shareholders and affiliates) waives all right to trial by jury in any action, proceeding or counterclaim (whether based upon contract, tort or otherwise) in any way arising out of or relating to this Agreement. Each party hereto agrees that a final judgment in any such action, proceeding or counterclaim brought in any such court shall be conclusive and binding upon such party and may be enforced in any other courts of the jurisdiction of which such party is or may be subject, by suit upon such judgment.

SECTION 14. Successors and Assigns. This Agreement shall be binding upon the Distributor and the Agent and their successors and permitted assigns and any successor or permitted assign of any substantial portion of the Distributor’s or the Agent’s respective businesses and/or assets.

This Agreement may not be transferred or assigned without the consent of the non-transferring or non-assigning party; provided, however, that no such consent shall be required to transfer or assign this Agreement to an entity controlling, controlled by or under common control with, the transferring or assigning party.

SECTION 15. Severability. Whenever possible, each provision of this Agreement shall be interpreted in such manner as to be effective and valid under applicable law. If, however, any provision of this Agreement is held, under applicable law, to be invalid, illegal or unenforceable in any respect, such provision shall be ineffective only to the extent of such invalidity, and the validity, legality and enforceability of the remaining provisions of this Agreement shall not be affected or impaired in any way and shall be interpreted to give effect to the intent of the parties manifested thereby.

SECTION 16. Investigations and Proceedings. The parties to this Agreement agree to cooperate fully in any securities regulatory investigation or proceeding or any judicial proceeding with respect to each party’s activities under this Agreement and promptly to notify the other party of any such investigation or proceeding.

SECTION 17. Modification, Waiver and Amendment. No modification, alteration or amendment of this Agreement will be valid or binding unless in writing and signed by all parties. No waiver of any term or condition of this Agreement will be construed as a waiver of any other term or condition; nor will any waiver of any default or breach under this Agreement be

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construed as a waiver of any other default or breach. No waiver will be binding unless in writing and signed by the party waiving the term, condition, default or breach. Any failure or delay by any party to enforce any of its rights under this Agreement will not be deemed a continuing waiver or modification hereof and such party, within the time provided by law, may commence appropriate legal proceedings to enforce any or all of such right.

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If the foregoing correctly sets forth the understanding between the Distributor and the Agent, please so indicate in the space provided below for that purpose, whereupon this Agreement and your acceptance shall constitute a binding agreement between the Distributor and the Agent. Alternatively, the execution of this Agreement by the Distributor and the acceptance by or on behalf of the Agent may be evidenced by an exchange of telegraphic or other written communications.

ACCEPTED as of the date

first above written

[Signature Page for Sub-Placement Agent Agreement for Western Asset Municipal High Income Fund Inc.]

ADDENDUM

TO

SUB-PLACEMENT AGENT AGREEMENT

BETWEEN

FRANKLIN DISTRIBUTORS, LLC

AND

UBS SECURITIES LLC

Compensation payable to the Agent for acting as a sub-placement agent with respect to a specified sale of Shares pursuant to this Agreement shall be determined by multiplying the Gross Sales Proceeds by the Applicable Selling Agent Commission as set forth below:

Where:

“Gross Sales Proceeds” with respect to each sale of Shares shall be the Gross Sales Price multiplied by the number of Shares sold;

“Gross Sales Price” with respect to each sale of Shares sold pursuant to this Agreement shall be the gross sales price per share of such Shares.