Definitely stop the sex life if you haven't already, for your own safety and get tested for STDs.
Once I knew my husband was unfaithful with (many) men, I asked him to choose between putting the brakes on this (so we could map out next steps sanely) or moving out. He moved out.
Over time, (2 years) things are easier. I find I actually like myself. He still remains firmly in the closet to family, friends, which really locks me in his closet too.
Next step in my mind, is to tell those who deserve to know. But he is pathologically trapped within himself. This will be very difficult.
Believe it or not, though, we still get together for bbqs, family, birthdays, weddings ... part of his cloak of normalcy.
I see it as this: I married a hologram. He was never really him. Now in our sort-of friendship I have to decide if I like this person. Sometimes I do. Sometimes I don't. But I now get the luxury of distancing myself from him whenever I want - somewhat liberating, but not as freeing as him being "out".