So he's cheated on you before, can't hold a job, cheats on you again, blames it all on you, and you don't believe that telling people the truth about what he's doing will help -- it will only make it worse?
I'll try to keep it short, but just to clarify...
Yes, my H did cheat on me about 6 years ago. The cheating occured while we were seperated. I didn't know it then, but he left me over an EA. He decided he was a failure as a husband, so he better leave me before he hurt me. His logic, not mine BTW. He confessed 2 PA that happened durring our seperation (I didn't know about either of them before he confessed), changed jobs to avoid OW, recommitted to the marriage, and did a very good job of letting me know where he was and who he was with up till May of this year, when A LOT of stress added up and left both of us disconnected and exhausted.
On the job losses... The first was a change in bosses at a job H LOVED. New boss wanted a friend to have H's job and made life very difficult for H. H decided to transfer to a lower position in a different city after his boss doctored some hiring papers to make it look like H had disregarded company policy. I have had this story verified by other people BTW, not only from H. The second job he lost was for a small retailer. The whole company shut down overnight. Failed to pay 3 weeks of wages and the final month of health benefits. That was when we went on food stamps for a while. Durring this whole time, H worked between 2 and 4 part time jobs. He was never 'unemployed,' but the job losses were devistating for him. It was after the 2nd job loss that he started to withdraw from family activities.
As far as him lying about me, no, I wouldn't say he did that. Exagurated about a lot of things, oh h*!! yes. But no outright lies, and I believe that he had convinced himself that everything he said was true and acurate. I may not be a perfect housekeeper, but I do well enough to starve out the roaches that lived here before we moved in. Even his claim about me not allowing him to parent was part like that. I had asked and asked him to do more with us. Eventually, I sort of gave up and figured he would join us when he was ready to. Instead he thought I didn't want him arround, conveniently forgetting how hard I had tried to get him to do stuff together as a family.
As far as telling people the truth, nope I don't think it will help in this case. H walked out of the house because he considered our marriage to be already over. However, because so many people already believe he is having an affair, H is not going to be able to keep his EA (or possible PA) a secret from his closest family and friends. He has been careless, thinking he was already gone, and too many people know or at least think they know what he has done. He will have to deal with a lot of shame regardless of his decision to stay or go. It has to be his decision though, not mine. And it will be the natural consequences of his actions he will have to deal with, not a punishment dealt out by me.