Short answer: Yes. Unlike CHIP, Medicaid can sit behind an employer plan: the employer plan pays first and Medicaid pays last for covered services.
Texas treats private health insurance as a third-party resource. Medicaid pays only after the other coverage has paid, so the family must tell every provider about both coverages and the provider bills the employer plan first.
Families on Medicaid must also cooperate with HHSC on other coverage, which can include giving information about an available employer plan and enrolling in it when the state’s Health Insurance Premium Payment (HIPP) program finds that cost-effective. In that case the state can reimburse the employee’s share of the premium.
Practical point for an enrollment meeting: an employee whose children have Medicaid should not assume the children must be dropped from the group plan. Keeping them on may give broader networks, and HIPP may help pay for it.