Am I wrong to try work things out with my cheating husband ?

My husband has been lying to me for the past year. He’s gone to take out different loans amounting to £30,000 without my knowledge. Upon finding out he tried to deny and lie about it. I recently found out a couple of months ago that he was cheating on me with a 19 year old ex student of his. Even brought her to our home when I was on holiday and told her we divorcing and he’s going to marry her. He said to her he wished our 16month old daughter is the girls mums. When I confronted him he tried denying but later came clean when he found out I spoke to the girl. He’s not apologising and wants to work on our marriage. Should I forgive and try work things out with him or once a cheater and liar always a cheater and liar?