Declaring his love for another person (repeatedly over two years!) is serious cheating even without sexual intimacy. He's trying to minimise this by claiming it wasn't physical, but it's a false distinction.
How is he still at home behaving like nothing has happened? He's been tearful (useless to you), remorseful (a good sign if it's genuine) and defensive (a very bad sign). He claims that it was just an emotional relationship, didn't mean anything, was a fantasy etc etc ... how does this square with his declarations of love? Was he lying to her? If it was meaningless why did he do it, knowing he was risking his marriage, hurting you, tearing his family apart? What's he doing to make sure it never happens again, to repair your relationship, to regain your trust?
Only he can tell you what happened (she has no obligation or loyalty to you and you have no basis on which to trust her). He refuses. You know he's lied repeatedly (TWO YEARS!) and you don't believe what he's telling you now. Some relationships can recover (mostly) from cheating, but the cheater has to be willing to do EVERYTHING it takes to fix things, however long it takes, with no timeline and no guarantees. Your husband - still lying, still defensive, still evasive, still acting like nothing has changed - is nowhere near that point. Ask him when he will be, or if you two should be discussing (1) splitting up or (2) an open / nonmonogamous "business arrangement" kind of marriage going forward.
The only one benefiting from the status quo is him. It's destroying you and he's letting that happen. Ask him to leave (go stay somewhere else, friends or family or a hotel) if you need time and space to think. As you're medicated for anxiety and depression, do you have a therapist you can discuss the marriage situation with? And (sorry) if you've been intimate with your husband in the last two years, get checked for STDs if you haven't already.
(Oh, and her being cc'd on correspondence to him from a potential employer makes no sense unless she also works for the company or referred him. How would his potential employer even have their job applicant's former mistress's email address to add accidentally?)