Native Health Access Improvement Act of 2019 This bill establishes a grant program for Indian health facilities and expands the applicability of certain federal health care provisions to American Indians and Alaska Natives. Specifically, the bill provides funds for and requires the Indian Health Service (IHS) to award grants to Indian health facilities for the prevention and treatment of mental health and substance use disorders. The IHS must establish a technical assistance center for grantees. The bill defines Indian for purposes of health insurance reform, exchanges, and subsidies to include individuals of Indian descent who are members of an Indian community served by the IHS and individuals considered by the Department of Health and Human Services to be Indian for purposes of eligibility for Indian health care services. Individuals included in the definition are eligible for special monthly enrollment periods on health insurance exchanges and elimination of cost sharing under individual health coverage for those whose income is not more than 300% of the poverty line. Under current law, only members of Indian tribes are eligible for these benefits. The bill also exempts Indians, as defined by the bill, from the tax penalty for not maintaining minimum essential health coverage.