A lot of posters seem to have missed (the prior thread?) the important information in the OP it wasn't just the lying and cheating which is bad enough in and of itself. It was also the incredible cruelty he displayed on finally admitting the affair.
@TotallyUninspired My story is slightly different to yours but with a similarly cruel DH, who then turned sweetness and love during the separation, only to do an extremely swift 180 back to incredible cruelty as soon as he thought he'd got a foot in the door again. It was fear of the financial hit he would take upon divorce.
In the end I was given a lovely rendition of the Script - "you might get someone to fuck you but no one will ever love you" (aye right, sez you, you horrible cruel bastard!) "You're alone because you're a terrible person" (um... looks round at friends and family, I don't think I'm a terrible person and frankly why in the ever loving fuck would I take his opinion on anything given what he'd done and what kind of a person he turned out to be. Maybe it was projection of his own fears on that one ha ha!), etc, etc. I actually did laugh in his face because I was expecting it (thank you MN Vipers!) and it was so unoriginal.
I made a thread here about him in the early separation and was advised very well and similarly to you basically not to fall for it. A few posters correctly saw that I was going to take him back, and most posters also correctly predicted the outcome ^ It took me a while, and the second round of cruel behaviour and words to realise that it wasn't a weird aberration, it was who he truly was.
I'm not even sure that I was a real person to him or if he was just so callous a person in himself that he just didn't care about other people's feelings, but either way it worked out the same from my end.
I agree with all other PPs:
Either OW dumped him, single life isn't suiting or he's figured out the financial aspect of divorce.
It's clearly manipulative shite he's saying now and it is all about him if you read it back to yourself. It's a big him pity party and he expects you to come dry his tears?
The PP who pointed out the fact that he didn't suddenly realise he'd made a mistake because you were the love of his life. No, he realised (ha!) that he and the OW were "unsuited"... so second best it is then, how lucky do you feel? No one wants to be a romantic seat filler.
Did he mention the upheaval to the children? Either during the initial awful behaviour or how it could affect them if you get back together/ give things a go and it not work? Agree with PPs it would be interesting to know if he has properly co-parented + paid maintenance during the last few months.
It's all about him really isn't it?
He blindsided you deliberately to provoke a knee-jerk reaction. It worked and you have found yourself agreeing to joint counselling and feeling validated from him saying things that sound alright on the surface, but as soon as you look closer expose him for what he is - a selfish, manipulative, cruel man who really doesn't give a shit about what he's done to you and the children.
He wants what he wants and he doesn't care how he gets it. He was so cruel to you (and your DC for the way he left you), now he's acting out this little farce of "you're the only one I can be myself around" 
(<- not envy), and "I acted terribly", "boo-hoo mental health" because he wants his comfort blanket (you) while he window shops for the next "better" thing.
FWIW having a mental health crisis doesn't equate to saying such cruel things, nor does it equal such rubbish treatment.
I'm so sorry, it's such a headfuck when you are right in the middle of it.
Do counselling, solo. Get the finances sorted, quicker is better before the real him shows up again!
You deserve so much more than this 