faff, relationships can be rebuilt after an affair, so I am absolutely not negative about that sort of thing but I think you should take the time to look at some of the many many threads on here from the past. With the greatest will in the world, and an understanding of your immense pain, you need to accept that it is HUGELY UNLIKELY that you are being told the truth about this right now. It is almost certain that he will be minimising, and very likely indeed he will be outright lying. This is what cheaters do. It's a panic, kneejerk response to lessen the pain for the other and cover up misdeeds and keep options open. The fact that you have described him as somsone who wishes it would all go away makes me pretty certain your partner will be doing this.
I understand that you will be veering massively on the side of making things work right now. The fact is (and I do not believe there are any exceptions to this) you cannot know this unless you know the truth about what has happened, because you cannot judge. And you also cannot really know this until you have truly, deeply and frighteningly considered leaving, properly. Otherwise it is not a choice to stay, it is a terrified, shocked pick me dance from the hell of someone else completely destroying your perceoved reality and replacing it with nothing.
The story of JonestheSteam on here is worth searching for, it's a positive one. You will find many, many of people lied to and minimised to at the point of discovery, who then spend 2 to 10 years trying to revive a relationship while brushing inconvenient truths under the carpet, with an under-invested, resenting cheater partner, and a neglected, bitter, broken and confused cheated upon partner. This is very very very common. Don't waste years of your life. This has to be looked at. Get yourself into individual counselling to bolster your esteem and get yourself a support network in place. I know you are going to feel ashamed and confused but you should tell people close to you if you have friends an family you trust. Keeping it as a secret isolates you, prevents you gaining objectivity and makes him your only source of support for the thing he has done to you. This is not healthy.
Watch Beyonce's Lemonade!
And we are here. There is not enough information in your posts to really take your hand and guide you through this as we could do here. For example this friend he did not want you to contact because she knew about the affair etc seems odd and weak as an explanation. Most people who know about affairs will not admit it anyway, or if they wanted to, they would have done unprompted, so I am not sure why he would be so concerned about contacting her as to admit it to you. Perhaps you could elucidate if you want to.
I am not trying to worsen your pain, I promise. I'm trying to reduce it long term by suggesting you really fact this thing and the reality of it now. I am so so sorry this has happened to you.