As far as we know, the spouse is not obligated to provide health insurance to the former spouse in case of divorce (unless special circumstances are involved, such as pregnancy, etc.).
However, the spouse that is left without health insurance may be given an option of COBRA. COBRA is a federal law which mandates that a person covered under a health insurance policy be given the right to continue that coverage, at their own cost, for a set time period if certain requirements exist. For example, if you obtain a divorce and your spouse had family health insurance coverage through his employer, the employer would have to provide COBRA coverage for you after the divorce. That COBRA coverage would require that you have the same health insurance policy, although your coverage would now be individual and not family. You would have to pay the employer's cost for that individual policy.
In fact, this question was supposed to be resolved during your divorce negotiation process, and be reflected in your final property settlement agreement.
If this is not the case we recommend you to consult an attorney to find out whether you can petition the court now to correct the situation.
Please be advised that Legal Helpmate is not a law firm and we do not give legal advice to the public.