In general, it is not a good idea to co-own property with your ex-spouse after a divorce. There are several reasons for this.
Real Estate owned by both parties during the marriage is often what we call a “tenancy by the entirety”. The simplest way to explain this is that the property is owned not by the husband or wife, but by the marriage itself. When you get a divorce, there is no marriage to own this property anymore. At that point, the property becomes a “tenancy in common”. This is no different than owning a piece of property with a business partner. You lose many protections afforded by a tenancy in common. Each party also owns a divisible interest in the property and could, potentially, sell their one-half interest in that property. The latter may be fixed by completing a new deed to create a joint tenancy with right of survivorship, but this still does not afford the protections a tenancy in common has.
Additionally, if the mortgage stays in both names and one party, usually the one continuing to reside in the property, doesn’t pay, the lender can sue both parties, not just the one living in the house.
Vehicles owned by both parties after a divorce is also a bad idea. If there is a debt against a vehicle, you can run into a similar issue to the mortgage scenario above. If the spouse who drives the car doesn’t pay the debt, the lender can sue both parties. More importantly, however, is that if there is a car accident, the driver is not the only person liable for damages. Any owner of the vehicle can be held responsible as well through something called vicarious liability. This is why in my divorces, I always emphasize that the parties transfer the title of the vehicle to the person keeping the vehicle, regardless of the debt thereon. A debt arising out a car accident can easily and significantly exceed any car loan.
In general, I advise against co-owning property after a divorce. It is possible to do so and sometimes it is necessary due to the financial circumstances of the parties. In any case, it is important to consult with an experienced attorney about this.