The only thing that I could tell you is that you need to file for Equitable Distribution, post separation support/alimony. Signing an agreement does not always keep this out of court…though that is what a separation agreement is supposed to do. It is a binding contract and I suggest you contact an attorney as soon as possible.
Legally, he is responsible for 1/2 the marital debt. If there is a mortgage and car payment then he is still responsible for it. Singing an agreement with you does not take his name off the deed or the car loan. He could argue that in the agreement that responsibility was turned over to you, BUT he’s not holding up his end of the agreement. He can not sue you for losing the house and he can not legally hold you entirely responsible for the amount on the car, it’s marital debt and unless it is refinanced into your name alone, it’s 1/2 his problem.
My question is this: Do you work or are you a completely dependant spouse? If you are completely dependant then I suggest filing for post separation support immediately to help with these debts. I do not have any suggestions other than contacting the creditors for the mortgage and car and talk to them. Maybe something can be worked out.
The real issue is that you are living in the home and the car is in your possession. It’s easier for your stbx to attempt to walk away from those debts since he’s no longer living there or using the car.
I also suggest that you record conversations and keep documentation of everything that is said or paid.