Your wife is a walking emergency...
I agree, his wife IS a walking emergency, but at this particular point in time, so is HE.
This is a man who is willingly allowing his wife to cheat on him, to lie to him and accepting her behavior from someone he loves. This is a man who seriously needs to look at his life and reprioritize it.
The child that may or may not be yours should be your first consideration. Find out. Get a paternity test...and if that child is yours, your first priority is to protect him or her. Growing up with a mom who has major intimacy, trust esteem problems is never easy for a child. Growing up with a father who lets his wife cheat, life and walk all over him is a bad example to set. Whether it's a boy or a girl, that child would grow up in your house, seeing her cheat, seeing her lie, watching you allow it...and would grow up to be exactly like either one of you. And honestly, right now, neither of you are a great role model to offer your child.
Your wife has some serious issues that she needs to deal with. SHE needs to deal with them. You can't help her, I'm sorry to say. You can't even convince her...if she doesn't willingly walk into a therapist's office and say, "please help me..." there is not a single thing in this world that will change her or her behavior.
But you can change YOU. You can take a good, hard look at yourself and at your life and try and figure out why you are staying where you are. There is a huge difference between loving someone and hurting yourself to love them. There will come a point when you will realize that you've had enough...that you are done, and that you deserve more. I can tell you from an outside opinion what I believe...but only you will know inside when that breaking point comes for you. You are being abused...perhaps not physically, but most definitely emotionally...and I can tell you, those are the scars that heal the slowest. Start healing yourself.