Q: My husband was employed and was covered under a group plan as well as Medicare. He is no longer employed and has elected cobra. However, his cobra plan has informed us that because he is covered under Medicare, he is not entitled under federal law to receive cobra benefits. Is this true? And if so, what about coverage for me because I was covered under his group health plan. A: Your husband ‘s entitlement to Medicare does qualify you to elect COBRA. It is true that he can not have both COBRA and Medicare. The amount of time you as a spouse can stay on COBRA is for 36 months.