Municipal Bond Market Support Act of 2019 This bill amends the Internal Revenue Code, with respect to the limitations on deductions for interest expenses of financial institutions that hold tax-exempt bonds, to: permanently increase from $10 million to $30 million the annual limit on the amount of tax-exempt obligations that may be issued to qualify for the small issuer exception to the tax-exempt interest expense allocation rules; require the limit for the small issuer exception to be adjusted for inflation after 2019; make permanent the rule that allows qualified 501(c)(3) bonds to be treated is if they were issued by the tax-exempt organization for whose benefit the bond was issued; and make permanent the special rule for the tax treatment of qualified financings used to make or finance loans to certain states, political subdivisions, or tax-exempt organizations.