If you are separated from your spouse, can he dropped you from the medical insurance before the divorce is final?

It depends on the state and county where the divorce is pending.  In Spokane County, WA, where I practice, as soon as a divorce action is started, the court issues an automatic order that prohibits parties from cancelling insurance without court order or agreement.  This helps prevent the problem you describe.  I've had situations where one party cancels auto insurance and the other party gets in an accident.  Spouse who cancelled may be liable for damages.

If a spouse is threatening to cancel or has cancelled insurance, the first step I would recommend is explaining to spouse that they should not do so or they will incur unnecessary costs, liability, reimbursement and possibly penalties as described below. 

Next, try contacting the insurer to see if you can get some help. 

If you are unable to get help there, you should either try and get a temporary order requiring him to keep you on or reinstate you. 

You can also get your own insurance or pay for care and ask the court to award you the cost of this in the final divorce order.