Sorry you have the need to be here but you are at the best place to help you get thru this. Lots of hard learned experience here.
First....from what you wrote, it appears you have a good chance of saving a marriage. The confession, owning up, and over the top efforts are a good start....but it is only a start. Both of you have lots of work to do.
I would start with both of you seeing different IC. Your initial objective with your IC should be to help you survive the initial trauma of infidelity.....this is different than healing. Right now you just need to survive it. Healing yourself will come later. And healing the marriage is after that.
He needs to start IC with the objective of finding out what is broken in him that would allow him to cross that boundary into infidelity. "I was drunk and foolish" is not the correct answer. Digging deep to find the broken part is the ONLY correct answer. The key to him finding the answer is first finding out what his reward was from the affair....what need was he getting met..... Then figuring out why he had that need to begin with. No....it is not because he wasn't getting that need met by you....whatwas missing in him and why. I have lots more on that subject but this would be a good place for him to start.
Personally, I would hold off on the MC until you have both reached a better place emotionally and mentally. True healing of yourself and your marriage is a very slow process that happens in very small unnoticeable increments that you only see the progress by comparing to where you were 3 months ago or 6 months and then a year and 2 years etc. and as long as you can continue to see positive steps..... Then you know you are on the right path.
Neither of you needs to start out this journey with expectations. Start with the attitude of exploring with an open mind Use this initial time to learn more about yourselves as individuals and work on being a better you. Then you will both be able to bring so much more to the table when you start MC. If you follow the process you may be one of the fortunate couples that comes out of this with a stronger better marriage....but at the very least you will be a better stronger you.
I say this with the knowledge that trying to do too much, too fast, only leads to disappointment which then turns to resentment......resentment leads to either infidelity, revenge, or the best case.....DIVORCE. I personally would take divorce over revenge or infidelity....just sayin.
You have a long way to go now....the joy of marriage is over and the work of marriage needs to begin. The reward of the hard work will be the rebuilding of a better you.....and hopefully a better marriage.