I think the bigger issue is which company would pay. As far as your husband failing to notify, it could be that he is waiting until the next enrollment period. This may be a better question for your new insurance company. I think they used to send a notice to the old insurer cancelling the old insurance, but I'm not sure whether this still occurs.
The above statements are provided as general information and not intended as legal advice. Each matter has its own set of unique circumstances that cannot be adequately addressed without consultation. You are strongly advised to hire an attorney licensed to practice law in your state to represent you.
You have no duty to his insurer or his employer. It is perfectly legal to have multiple health insurance plans covering the same person. It may not do any good but it also isn't harmful to you. After the divorce your ex-husband could have removed you from coverage but that's between him, his insurer and his employer.