Citizen and lawfully present family members can get health insurance coverage through Medicaid, CHIP, and marketplaces even if other family members are not lawfully present. Family members that are not lawfully present, including undocumented immigrants, may apply for health insurance on behalf of citizen and lawfully present family members. For example, an undocumented immigrant parent may apply for health insurance for a citizen child.
When a family with mixed immigration status applies for health insurance, it only has to give citizenship and immigration status for those family members applying for coverage. Non-applicants, such as a parent applying for a child, do not have to provide citizenship or immigration status. Non-applicants will be asked to provide a Social Security number, but do not have to provide one unless the family is applying for help with costs for marketplace coverage and the individual is the tax-filer for the household. (42 C.F.R. § 435.406; 42 C.F.R. § 457.320).
Note that in October 2018, the Trump Administration proposed an expansion to the current policy that determines whether certain immigrants would be considered a “public charge.” While the rule is not finalized, it may eventually impact individuals seeking admission to the U.S. or seeking to adjust status to lawful permanent residence (green card) applying for or using certain public benefits, like Medicaid. Under current and proposed rules, the application and use of premium tax credits and cost-sharing reductions are exempted from the public charge determination test. If the rule is finalized, you will have time to act before the rule goes into effect, and thus can still apply for and use public benefits including Medicaid in the interim.