How can I get my heavily indebted husband's name off a house we currently both own?

House is in NH. We were going to move there. It didn't work. We're back in NY; still have the house. I paid downpayment ($100,000 out of $225,000) & closing costs from a bank account that pre-existed the marriage, which I kept separate. When my husband's NH business plans didn't pan out, I largely paid the mortgage, while we there & beyond out of money I inherited. So, I've always felt the bulk of the house is mine. Now, my husband (who is feckless in business), has signed a business related personal guarantee for a $110,000 plus legal fees, if a failing business he's involved with can't pay the money back. This on top of IRS debt he entangled me in, by not reporting a French bank account (unbeknownst to me). I'm fed up, & at 65, worried about the impact of debt on my financial security. I'm considering divorce. Will getting the house in a divorce protect it? Or, can we stay married & he sell his share of the house to me? Married, I get French retirement benefits.