Ouch, as awful as that story is, that's a "storybook confession" from H that very few LBS's get. Congratulations on your DB work! After my W's EA, even though we have reconciled she's never apologized or even acknowledged that what she did was wrong. That doesn't seem to happen much, so that's great news for your sitch!
Rebuilding your trust is a process that is often two steps forward and one step back and will be very hard on both of you.
I recommend you Google for "Affair Recovery", there are many web sites that spell out practices that will make your recovery easier for both of you. Two of the most important things are that (1) H must vow to go "no contact" with OW now and forever, including changing jobs if that's what it takes, and (2) H must provide complete transparency to you WRT phone, email, and travel schedule. Number 2 is not a permanent arrangement, just until you are able to rebuild your mutual trust.
Now, WRT H's affair. First of all, EVERY marriage has issues and weaknesses. This would still be an excellent time to evaluate your own contribution to the issues in the marriage. It's best if you don't look at the affair as "all H's fault", but instead look at it as a crisis in your marriage that you BOTH contributed to. If you view it that way, it's not all work H has to do to make it up to you, it's a shared challenge that you both need to strive to have a better marriage. I do believe you've started down this road, don't let H's confession be an excuse to give up your own changes -- keep working at it!
Also, remember that H is human, not some monster. If you can "normalize" H's affair it will help you to get to forgiveness. We all like attention from the opposite sex, we all like to feel attractive, we all like to feel wanted and needed, those forces have a very strong pull on all of us. If you were not completely satisfied with H, and you worked with an attractive man who you really got along well with, who made you laugh, and who made you feel good about yourself, it's reasonable to expect that you'd enjoy spending time with that person. If you then came home to H and he was involved with the kids, working on paying bills, and just not spending that much time with you, then OM may seem much more fun and interesting to be with by comparison. It's usually not a decision to be unfaithful, it's a slippery slope that people slide down an imperceptible amount each day until they realize they are way over the line and don't know how they got there. He didn't do it to hurt you, he made some bad mistakes, and he is human. This does not excuse him or say that it's ok, it just says that "it happens, we're human".
Three suggestions for you:
1) There is a good book called "After the Affair" that can help you navigate your path forward, I recommend it.
2) There is another book called "Why Good People Have Affairs" that may help you understand what's happened. Don't read that now, it's too soon, but maybe pick it up in 4-6 months.
3) You will need to establish with H a mutual "contract" about what exactly will be considered "over the line" going forward. You should agree that if either of you are feeling tempted, that you will talk about it openly and honestly and that it will be OK to do so. In terms of where that line is drawn, there are some excellent resources on Pat Love's website. Go to the "Downloads" section. There is a word document about what defines an "office spouse". Download that and review it. She also has some excellent questionnaires that you can work through together to help you to reconnect.
Good luck and let me know how else I can help.
Accuray
Married 18, Together 20, Now Divorced M: 48, W: 50, D: 18, S: 16, D: 12 Bomb Dropped (EA, D): 7/13/11 Start Reconcile: 8/15/11 Bomb Dropped (EA, D): 5/1/2014 (Divorced) In a New Relationship: 3/2015