Op... how much of the work is finished.... or whether there is still work to make it 1) habitable.. 2) more comfortable.
There's a distinction there in that habitable means you could still live there and carry on making improvements that might make it easier to sell if that's what you want to do.
Alternatively. if it was finished you might be able to rent it out. For example . Houses round here are in demand, the rents are far higher than the mortgages (or were before Liz Truss) and get rented by companies for overseas employees and its good money and the house will go up in value at the same time. These are often temporary contracts of a year or two.. So you might then have more room for manoeuvre.
It strikes me that your DH has already made poor investment decisions... and now walking out and washing his hands of the house project (which is what it is) ... is about to make another, even more costly, poor decision.
The house you bought together, which has presumably had considerable improvements done to it, is an asset.. even though it may feel like a money pit and it is up to BOTH of you to look at your options to either keep the asset and let it continue to grow in value as you continue to work on it yourselves...
Or decide how to maximise the amount you can now sell it for, or possibly how to minimise the loss..
Talk to estate agents.. ( don't tell them the whole story.. just ask for valuations and say as LITTLE as possible about your own situations.. maybe something like... We've been offered a potential job abroad and we are still thinking about it.. what would renting require and how much would it be worth... This may sound a bit dishonest.. but having been through the mill with estate agents some are great , but some are the sort that you never want to give them the impression that you are desperate to sell.
Do your own research as well.
I understand why you are focusing on the house, rather than the relationship right now.. as its the roof over your head and the most immediate problem. It sounds like you are still in shock and literally trying to work out what to do about what seems like an unconquerable problem. Given that your DH has literally walked out and said its all your mess deal with it.
Your situation is complex, but all you can do now is pick away at it bit by bit. Step by Step. Do your research and try to find options and Don't let him just dismiss every suggestion out of hand because he's angry, or because he feels this is more manipulation. Someone has to be the adult and try to find a way though this.
At some stage he will have to face reality that it is a joint asset and he needs to communicate and co-operate make sensible well thought out logical decisions about how you can both sort it out, rather than make your joint losses even worse.