I think it really all depends on context to be honest.
When the situation is "understandable" and people are brutally honest and open about things then yeah, maybe.
It's a rocky path that you're going down though, and I personally think in your situation what gets me is the REPEATED lying. It wasn't just one lie, it was repeated.
You threw him out, and he then ended things with her (or her with him - you'll never know) and suddenly he comes back and wants to build bridges.
This, in my opinion will not survive.
If it was going to survive it might look like:
He admitted the affair, told you everything, dumped her immediately, organised counselling, built bridges and moved out while he did.
From what I see here, he has only come back to you when things finished with her, his first thought wasn't "i made a mistake", his first thought was to keep seeing her.
You're wasting your time and energy on this one and this is going to implode. You were right the first time when you threw him out for the lies, and for the repeated lies, and then for him continuing on with her when he left.
He isn't sorry.