First, I am very sorry that you're going through this. Do not deny or try to hide your feelings from yourself or your H. Cheating is like a loss, you will grieve, and you will still think about it for some time to come. It can be a very big wake up call, but you also have to handle it the right way going forward.
Cut off all contact with this "friend", and make sure he does too.
Complete transparency - on both your parts (FB/email/texts/etc) He should have no issue with you having access to everything. You have to start rebuilding trust.
Don't stay together for the kids. Evaluate your relationship. Kids are happier when their parents are happier.
Cut back on drinking or cut it out completely if you are both drinkers. You need real, honest conversations right now.
Don't be afraid to get the details if those questions are tearing you up. Get the when, how long, where, how did it start, what do you think made you do it, etc. Don't expect all the answers right away, but get to the root of the problem or this will never work.
COUNSELING. Seriously. For both of you, together and individually. Don't put this off.
Best of luck to you. A lot of people will likely tell you to pack your bags and get out. From personal experience, I don't believe that should always be the case. But, don't get ahead of yourself. You both have years of healing and progress to be made in your relationship and individually.