The rules are somewhat different depending on the plan your parents have.
If your parents are covered under a small employer plan (less than 50 workers) provided by an insurance company through the Marketplace or outside of the Marketplace, or if your parents are covered under a nongroup policy they bought themselves, then your parent’s plan is required to cover your prenatal care and delivery.
However, if your parents are covered under a group health plan offered by a large employer (50 or more workers), then your parent’s plan is only required to cover your prenatal care, but is not required to cover the delivery. Medicaid covers prenatal and delivery services in all states. You could see if you can qualify for Medicaid on your own.
Your parent’s plan, regardless of the source, generally won’t be required to cover your child as a dependent. You will be responsible for obtaining coverage for your baby. Depending on your income, your child may be eligible for coverage under the Medicaid/CHIP program in your state. Or, you can buy a family policy through the Marketplace and, depending on your income, you may be eligible for a premium tax credit to reduce your cost of that coverage.