Territories Health Equity Act of 2019 This bill alters provisions under Medicaid, Medicare, and Medicare Advantage relating to U.S. territories, and generally modifies and establishes programs to expand health insurance coverage for residents. Among other things, the bill eliminates Medicaid funding limitations for U.S. territories beginning in FY2020; repeals provisions that exclude residents of Puerto Rico from a certain automatic enrollment process for Medicare medical services; establishes minimum criteria for certain elements used in Medicare Advantage payment calculations for areas within U.S. territories; and allows residents of U.S. territories who are unable to obtain health insurance through their employer or a health insurance exchange to instead obtain coverage through the District of Columbia exchange, including coverage that is available to Members of Congress and their staff.