I really don't think you're going to get what you want from counselling.
At best he'll admit to a little more and parrot back to the counsellor "yes I can see now that it hurt her".
If he thinks you're actually going to leave him and he doesn't want to deal with that (and it won't be because he loves you, because if he loved you he wouldn't cheat on you with prostitutes) then he might muster up some crocodile tears to persuade you. Be warned - after that, any issue you have in future will be met with "we have to move on, I did counselling, I said I'm sorry, you can't keep punishing me, you're annoying me now". You know this is true.
Thing is, it's bloody obvious from your posts here that you're desperate to stay together, that you're willing to accept this shite. If it's obvious from words on a page, trust me it's obvious to him. I think the minute a woman says "counselling...?" a man knows he's home and dry, and is usually right. I really do suggest that any counselling takes place with him living away. Obviously doing 50/50 on childcare though!
You making him do counselling don't stop him hurting you again (well, if you find out) and it won't stop him doing it to other people.
My XH has never admitted to more than just looking, I booked but I never went through with it. He is doing it still, despite having a new GF. I told him I knew and to stop - told him I'd used an investigator (not quite true) and named two of the prostitutes (stage names) he'd booked in the last month. His text back? "I can assure you I haven't done anything". That's what they say when you NAME the women!
Your husband has no incentive to be honest with you. Why would he?
And if you're thinking "you can assume mine is like yours" please bear in mind that there really is a type, a script. You've already seen this in what we predicted so far - minimising and gradually admitting to a little bit more.
FFS, your particular arsehole even told you it wasn't cheating!!! You have no chance of discovering he's actually a decent chap really.
I'm sorry, I know this is horrid to hear and I'm being very blunt. But you have to understand the life you're agreeing to; you'll never know what happened, he won't feel guilty, and he will carry on doing it.