Background
Jane and I belonged to the same group of friends since childhood. In this group, we all used to hang out, go camping, all kinds of stuff. Despite all of us eventually growing older and parting ways, most of us stayed friends and would hang out regularly on holidays, still go camping in summer and so on.
Jane and I started dating when I was 16 and she was 14. We dated for 7 years, last 2 years living together. During the time we were living together, we would often hang out with Mike, another friend from the childhood friend group. One year before our break-up, she cheated on me with my then best friend Bob. Despite me willing to forgive her and move on, she wanted to break up, but we eventually agreed to try again.
After a rather ugly year of her doing stupid things just to make me angry and me being afraid to say a word without triggering another episode of threats of her leaving me, she finally broke up with me and moved out. Despite realizing that it was the inevitable outcome at the time, I was devastated. Our issues were not caused by abuse/violence or things of that nature.
I found out through a mutual friend that a few months later, she started dating another of our friends, Mike.
Problem
Her dating Mike, in fact, did not surprise me that much. What surprised me was that I had to learn about it from a third party, since I would expect (and very much prefer) Mike to approach me and tell me about it face to face.
I realize that what she does is not my business anymore and I have to deal with my feelings. I am quite introverted (I did not make new friends since high school). If I want to keep my very few friends (which I do), I am bound to come across the couple eventually.
I don't have to interact with both Jane and Mike, but I want to. Chances are that if I wanted to break any contact with them, I would lose all my friends. I would like to keep in touch with these friends and keep hanging out with them regularly.
I want to keep my friends (including Mike) and basically not address the fact of them dating. That would be awkward for everybody, so I am looking for a solution which would do the least damage to friendships and still keep my face.
My issue is that given our history, I have no idea how to interact with them when it comes to it. What would be a mature way to handle it?
If relevant, I am now 23, Jane is 21, Mike is her age and we are located in East-Central Europe.