I don't think anyone can tell you what you should do - you say your relationship is good now, and that may well be worth hanging on to.
I can tell you how I would feel - for me it would be a deal breaker. First and foremost because when you were suffering from PND- a horrible thing to deal with, he made it about him and how hard it was for him, and sought 'solace' elsewhere. Where did you get your solace? - when you needed him most he was looking at another woman.
Secondly - he almost certainly slept with her. That would be a deal breaker for me (I would have zero tolerance) but I know some people can move past that if it was a ONS. The lying about it and the claiming not to remember would be the hardest thing for me to deal with, and the emotional affair he had with her.
I also subscribe to the 'once a cheater always a cheater' - from personal experience . But I realise that is only my personal experience and others may tell you that cheaters can reform.
So it is the 'you were ill, it was very hard for me and so I went with another woman' that I would find unforgiveable, It is such a totally self absorbed and unempathetic attitude. He was your partner, he should have been looking after you when you needed him, what if you become ill again - will he feel justified in looking elsewhere? Ask yourself if he were very ill would your reaction to his illness be to find another man?
I think that is where you anger lies, and that is what you are struggling to get over, You have lost trust and confidence in him because you know that when the chips are down he can't be relied upon to be there for you.
That might be something you can talk through and resolve, that is your call, but I do think that if you don't address the whole episode with him your anger will fester.
And he cheated on you - so you have a right to ask whatever you want, to have your feelings heard, and to do it in your time. he may want to sweep it under the carpet and pretend it never happened, you don't have to do that if you need to work through it.