I agree with the prior commenter. Most plans will terminate COBRA immediately on your being covered by your new employer's plan if that new coverage starts after you have made your COBRA election. It is possible that Anthem realized that your COBRA coverage was no longer valid, and they may refuse to process your claims at all on that coverage. COB with COBRA and another plan only makes sense when your other coverage was already in place before you made your COBRA election. In that case, I would agree that the participant/dependent rule applies.