Maximizing Outcomes for Moms through Medicaid Improvement and Enhancement of Services Act or the MOMMIES Act This bill establishes a series of programs and requirements under Medicaid and the Children's Health Insurance Program (CHIP) relating to maternal health. For example, the bill expands eligibility for coverage under Medicaid and CHIP from 60 days to one year after the last day of pregnancy and requires such coverage to include oral health services. The bill also establishes a demonstration program in which states receive grants to implement or expand models for maternity care homes that provide services to Medicaid or CHIP beneficiaries. The Government Accountability Office must report on (1) gaps in coverage under Medicaid and CHIP for pregnant and postpartum women, and (2) the use of telehealth by state Medicaid programs to increase access to maternity care.