Sorry, red flags on this one. Her losing her job is their fault, not yours- do not let him guilt you into that. What she is doing is highly unprofessional- given her occupation. She is seeing people who are emotionally unbalanced and it might even go further next time. She could prey on someone else.
I'm telling you- if he's telling you he doesn't know if he wants to work on the marriage- and that if you expose their affair it's over between you??? Huge red flags. All cheater say those things.
Truth of the matter- your marriage can survive him being mad over exposure- it cannot survive when he's in an affair.
He should have thought about getting in trouble before he betrayed you.