It is good that you spoke with your kids, but I think you need to tell them the truth of why their father is leaving. You need to explain to them that their father has a girlfriend, and that just isn't allowed in marriage. Someone must show them what marriage is supposed to be about, and that someone must be you.
If you don't explain this to them they are going to be confused. They are just going to think that you and their father weren't a good match or whatever. Or that if someone in a marriage isn't happy it is o.k. just to leave. Their father is having an affair. That is why he is leaving. Further, the kids will find out the truth eventually and they aren't going to be real happy that you lied to them.
You really need to stop protecting him from his bad decisions. And If your husband isn't self-employed, you need to tell his work about this . . . especially if he supervises this "woman". The company could be in trouble is their little fling goes south . . . like sexual harassment lawsuit trouble.
Don't help this man break up your family. Don't protect him from the fallout from his bad decisions. I would tell everyone what he is doing. All your friends, all his relatives, all her relatives, their work. If she is married her husband needs to know too. Exposure is toxic to affairs. I would start doing some.
I'm a man . . . But I can change . . . If I have to . . . I guess . . .