Here are the few details as to how other insurance works with Medicare Part D (Prescription drug coverage). Medicaid : If you have Medicare and full Medicaid coverage, Medicare covers your Part D prescription drugs. Medicaid may still cover some drugs that Medicare doesn't cover. Employer or union coverage : This is health coverage from your or your spouse's or other family member's current or former employer or union. If you have prescription drug coverage based on your current or previous employment, your employer or union will notify you each year to let you  know if your prescription drug coverage is creditable. Keep the information you get. Call your benefits administrator for more information before making any changes to your coverage. Note: If your join a Medicare drug plan, you, or your dependents may lose your employer or union health coverage. COBRA : This is a federal law that may allow you to temporarily keep employer or union health ...