Unfortunately, no. This can be a stipulation in a child custody or child support agreement following a divorce, but as for spousal support, your ex-husband does not have to keep you on his health insurance.
There is a silver lining, however. Once your divorce is finalized, there is a chance you could be eligible for benefits under the Consolidated Omnibus Budget Reconciliation Act—also known as COBRA—if your spouse works for a company with 20 or more employees. This means that you can get continuation coverage for up to 36 months (three years) following your divorce. You can expect to be charged for this coverage, but the employer cannot charge you more than 102 percent of the premium for its employees. Note, however, that amount is 102 percent of the whole premium, even if your ex-husband pays only part of that premium by paycheck deduction.
If you do decide to take the temporary COBRA coverage, you will need to accept it within 60 days of your divorce being final. If you do not accept the health insurance during that time, you are forfeiting the opportunity.
Something else to consider before accepting COBRA coverage is if you face a serious illness or injury during that temporary coverage period, you may have trouble finding good health insurance once it expires because of your pre-existing condition or past health history. If you are in relatively good health when your divorce is finalized, you may want to look for your own health insurance just to be safe and covered. Keep in mind that you can accept COBRA insurance and then drop it at any time during those 36 months.