I dont know the laws in the US - so you need to see a lawyer cos to me it dont look good
My 1st thoughts are
The house is part of his assets (cos his name is on the mortgage he is co-owner - dont matter who pays it)
Since you say he is your "ex" - what "ex" would that be?
If he is your "ex"-husband what was agreed in the divorce papers?
If his debt is large enough the creditors may be able to force a sale of the house to get back some/all of what he owes
How MUCH of the proceeds of the sale depends on a number of things
5 things dont help
1) he dont live there so its not "his" home and he is your "ex"
2) you are in arrears with the mortgage
3) YOU agreed to him not paying the mortgage (in exchange for not collecting child support) - so YOU contributed to the situation as regards the arrears. (Presumably this was done via mutual agreement and not via the courts)
(I think legally you would have been better taking out your own mortgage and buying him out, AND collecting child support)
4) He was paying the mortgage for some time - thus preserving his rights to the equity in the property even though he had become your "ex" and moved out (this goes back to 3)
5) he has been refused chapter 13 therefore his only choice is chapter 7 - Under this the house can be seized - Him not living there makes this more likely - The mortgage being in arrears makes it even more likely you are gonna lose the house
(the mortgage company are more likely to foreclose before the court orders its sale)
What I dont understand is
How on earth do you expect to refinance? - Only way you COULD refinance would be to take out another mortgage to cover the outstanding debt on the current mortgage AND the 30k arrears which you say you cant afford.
(and this could only happen if he WASNT going for bankruptcy,cos at THIS moment the house is part of his assets and what happens to it will be decided in the bankruptcy hearings)