Can he make me have to pay half?

My ex and I were married 10 years and have 2 children together. After years of fighting I told him I wanted a seperation and one of us were going to have to leave. He was unemployed at the time but I knew he could go stay with his parents a few miles away and still see the kids often. HE said he didnt want to move out of his (the) marital home and so he went around with me to find a place to rent for myself and the kids and I signed a 1 yr lease on a house. Because his credit was much better than mine 3 years ago when we bought the marital home, the bank wanted to put the mortgage only in his name but it was titled in both of ours. Unfortunaley 2weeks after our move he lost his job and then decided he didnt want to have a boss anymore so he dabbled in trying to start small home business, none of which worked.
Since this time we have been granted our divorce but are still dealing with distribution of assets. I helped him pay his bills and the mortgage for 6 months and stopped because he had not even looked for a real job to support himself or our two kids that lived with me. The mortgage company approved his request to have his mortgage modified after a few months of the payment not being made (even though he had the money in a saving account but spent it on “thing”) for more manageable payments for him (almost half of original payment amount). I found out thru his sister that he had stopped making any house payments when he got his job with the intentions of letting the house go into foreclosure because he no longer wants the house. He is claiming that he now wants me to agree to pay for half of the penalty amount of the foreclosure/shortsale/tax liability that he may or may not be assessed, because HIS house is now OUR problem and a marital assets/debt. We were not able to settle this in mediation and now have to go in front of the judge. I dont want the house and can not afford the payments even if i wanted to as I lost my own job a few months ago. Do I have any recourse or defence for his demands?

If the problems with the mortgage arose after you separated the extra debt and additional fees are his burden alone.

Can you cite any case laws that support this as I am now representing myself

Citing case law is beyond the scope of this forum. I would suggest you read the statue on Equitable Distribution (NCGS 50-20).