Q: I was laid off but have medicare canI take cobra for my wife and 19 year old daughter who is a full-time college student? I was told that I would need to take cobra also. A: Once you are entitled to Medicare you are no longer allowed to continue on the employer ‘s group health plan through COBRA. You are not able to have Medicare and COBRA. However, your spouse and dependents will still be eligible for COBRA . On the COBRA election form from your employer it will allow you to continue the coverage for your spouse and dependents.