I was in your shoes a few weeks ago. Was told exactly the same thing, literally verbatim the way you have described it.
But for us, this was after 2 years of trying to put his affair behaind us. And I thought we were doing well. Wrong.
DH left to get some space, which has now progressed into official separation. And oddly enough he's being going out with a friend from work - for company you understand.
And I believe not a single word of it.
Anyway - I'm not sure I can add to what you have already been told, and I hope things go differently for you.
I would say that one mistake we made was thinking we could manage without counselling the first time around. Part of your problem is that your DH is comparing the first flush of infatuation/lust with what you have developed over years. And it is a kind of fantasy land, an escapism for him. I think that in order to fully get away from that he needs to talk to other people about it, to make it part of reality. I'm afraid that you probably aren't being told the whole truth about this woman, and if that comes out he'll tell you it's because he cares about you and was trying to save you from hurt. But really he's trying to cover his arse.
For me, I can now acknowledge that I would not risk going through this again with my DH, even if he were to change his mind. I know I have done my best to preserve our marriage for our DC's sake over the last 2 years, but it seems I was the only one doing so. So while I am hurting, and I do love him despite everything, I know that this is best for me in the long run.
So if your DH decides he wants to work with you to fix what he has broken, make sure he talks to someone, and that you realise that it is up to him put in the hard graft. Paying lip service to the 'of course I want to make things work' approach is not enough, and long term will not work.
Pay more attention to what he does now, rather than what he says.
I'm trying very hard here to come from a balanced perspective, but given my own situation I'm not sure how successful I have been. But I have had an amazing amount of support here on MN, please make use of it too.