This is one of those times where you need to put your emotions aside. Be practical, you have a daughter to think about here.
The facts are that you barely know this man. He is a drug addict and because of him you now have debt.
You need to be practical. Can you afford the debt on your own? How much is it? If you can't afford it, call the company you owe the money too now and discuss it with them. By being proactive they are likely to negotiate with you and arrange a manageable payment plan. I think you need to work on the assumption he won't be paying the money back but if he does, consider it a bonus.
Get him out of your house. My guess is he'll beg for a short amount of time before showing his true colours and start being horrible to you.
See a solicitor to check he cannot claim for anything and make your separation official ASAP.
Oh, and in case you are feeling a little guilty - you promised to support a drug addict who was in recovery, who you thought was a faithful husband, someone you thought you were in a team with. He is none of those things.
He on the other hand, lied, cheated, let you take on his debt and has tried to emotionally blackmail you into staying with him.
Tell whoever you want. Surround yourself with support