I agree with Kerry...I'm not sure meeting them both together would do much good for anyone...that said, I know that you'll find the best course of action for you and your children - just remember to take some time with your decisions - giving yourself a day or two (that 48 hour rule) to allow emotions to settle before you act on them too quickly.
When my STBX had her affair a few years ago, eventually did what you did - I saw all the exchanges between them - from text messages to emails - and it was grueling - particularly because it was never enough...it was just enough to hurt me - but there was never any kind of answer in those words between them - just the awareness that she was lost to me in some way...I took her back after that - and sometimes I think it was my mistake...since I never allowed her to look at herself the way your H must now look at himself.
You're a good person, Kalni, so of course you feel compassion for his pain - but just remember that he knows how to manipulate you - he knows how to get into your heart - and he knows how to bring you around to his point of view...and he knows how to use that for himself. Right now, he's suffering and is probably terrified at the prospect of having to live with the huge consequences of his actions - of course it makes him feel remorseful and want to cling to what he had...you can acknowledge that - but please don't do anything to indulge him...find more ways to put your energy and attention back onto you and your children - and put away that other life he had - so you can continue to live your life more fully.