Black Maternal Health Momnibus Act This bill directs multi-agency efforts to improve maternal health with a particular focus on racial and ethnic minority groups, veterans, and other vulnerable populations. The Department of Health and Human Services (HHS) must address the social determinants of maternal health (i.e., child care, housing, and other nonmedical factors that affect health outcomes). HHS and other departments must also carry out other actions to increase access to maternal health care and otherwise improve maternal health, such as growing and diversifying the maternal health workforce; establishing various grants and other programs, including ones related to maternal health disparities and maternal behavioral health; testing alternative payment models for perinatal care in Medicaid and the Children's Health Insurance Program (CHIP); addressing maternal health during public health emergencies; and supporting training, technology, and telehealth initiatives. The bill further provides for extended postpartum and breastfeeding eligibility for the Special Supplemental Nutrition Program for Women, Infants, and Children; increased research and data collection on maternal health indicators; activities to mitigate adverse maternal health outcomes associated with climate change; and expanded public education to improve maternal vaccination rates. The bill also addresses maternal health for incarcerated populations. For example, it (1) requires the Bureau of Prisons and the Department of Justice to establish programs to improve maternity care; and (2) reduces grants for criminal justice activities unless the recipient state or territory has a law to limit the use of restraints during pregnancy for incarcerated populations.