Your parent’s plan, regardless of the source, is generally not required to cover your child as a dependent. 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 and whether health insurance is available from your own employer, you may be eligible for a premium tax credit and/or cost sharing subsidy to reduce your cost of that coverage.