Do I have rights to my husband’s vehicle even if were separated?

You can use his vehicle in his name if you are still married and have a community interest in the car. BUT, if you are separated, be very careful that he does not report you as having stolen his vehicle if you are driving it. If it's in his name, you may not be able to prove to the cops that you have an ownership interest through marriage. People have a bad habit of turning on each other when they are "separated."

It is a marital asset so you can use it, even if it is in his name.

If the vehicle was purchased during the marriage, and the vehicle is in your husband's name, you continue (unless there is a court order stating otherwise) to have equal access to all of the marital property.