When you file for divorce, the court has Automatic Orders which generally begin immediately. One of those Orders is, typically, that you can't drop a spouse from insurance.
If the car he has is not
in your name--but in his only
, you may want to drop him from your policy before he screws your premium up for the next 5 years or more. If the car is in your name as well, then you have
to keep it on your policy for now.
However, you can ask the court for a Temporary Hearing as soon as you file. Tell the court at the hearing of his alcoholism
problem and ask for an immediate Order that he take sole possession of the car---that the registration be changed to indicate you are no longer an owner, and that you may take him off of your car policy to protect yourself.
He will likely be able to stay on the health policy for the immediate future, and if you take him off of it right now, there is a possibility that the court will order that you either put him back on--or pay for new health insurance out of your own pocket---so be careful there. Often a spouse once taken off a policy can only be put back on during the annual sign-up period