Personal Injury Lawyer
There is no requirement for your spouse to carry you on their insurance policy. You can file for spousal support and request the court order this to occur as part of an award of such support.
Family Law Attorney
Robert is correct, but I would add that you should file for post-separation support sooner rather than later, or if your spouse is willing to work with you, then you could agree to a separation agreement that would have them continue to cover you on their health insurance.
After the divorce is granted, you are entitled to Cobra benefits for 36 months.