Moms Matter Act This bill establishes two grant programs to address maternal mental health conditions and substance use disorders, with a focus on demographic groups with elevated rates of maternal mortality and morbidity, maternal health disparities, and other adverse outcomes. First, the Substance Abuse and Mental Health Services Administration must award grants for maternal behavioral health services and education and training for health care providers about maternal mental health conditions and substance use disorders in pregnancy. Eligible grantees include (1) state, tribal, and local governments; (2) health care providers; and (3) organizations that serve pregnant and postpartum individuals. Second, the Department of Health and Human Services may award grants to grow and diversify the maternal mental and behavioral health workforce by establishing or expanding schools and training programs.