Jasmine, Encouraging your H to discuss the affair will help him get out the secrets he his holding onto that may make him feel like he could do it again, at least that is how I felt in my case.
When my W found out she was very sad and hurt, she asked alot of questions, and I answered some truthfully but I blurred some of the facts or just denied others. Acouple of months later, when I felt like things had calmed down enough at home I picked up right where I left off. Because of this we are in a horroibel situation.
After being discovered a second time I have admitted to everything, and I feel complete relief for it. No more having to dodge questions or try to remember the BS answer I gave. I really wish I would have just told the truth the first time, because I can now say with 100% certainty thay I will never stray from my W again if our M survives this troubled time.
Just another word of advice, don't be afraid to be angry about the A, my wife didn't get angry when she found out the first time, and it took her about 3 weeks to get angry this time. Even though her anger is tough on me it is what her and I need if we are going to move forward.

Be honest with your H about your pain and ask him to be honest about his reasons, but be careful to only ask the questions that you can handle the answers for. Sometimes the truth is not as bad as what you have imagined, and other times it can be a whole lot worse.

Good luck, I'm rooting for the both of you.