Can my husband drop me from his insurance before we are divorced?

While it is probably unwise for him to do so, if there is no court order requiring him to keep you on his insurance, there is a legal requirement that he name you on his insurance. And once you get divorced, if you do, he will no longer be able to cover you. While you are married any medical expenses you incur would probably be considered to be family expenses, and he will be liable for those expenses as you are too.