I was there when he FaceTimed her to end it and it was a quick call but then she started texting and called for another FaceTime. This time she was angry/upset etc asking why professing her love for him as he did as well but blamed the break up on distance. He didn’t tell her he was married with a baby. I didn’t pop into the phone or anything either. The second conversation ended with her asking him why and etc. so since we were in the car going home from the doc office he said he’d block her. He drop me off to bring his mom for another appt and he was suppose to come right back but felt long so I text him where are you and he said they talked again but this tine I was not there and I was furious. When he came home I he said he told me that if they talk again he would let me know but it seem like she was still pursuing something with him I lashed at him the moment he stepped into the house to text her the truth. That he was married and have 7mth off was the real reason not distance. Whatever was said on the FaceTime when I was not there seemed to have sealed it for her because she responded to him goodluck with that life. He then blocked her and deleted her as a contact.
Typically, the reason a WS wouldn't give the truth at the time of the "break-up call" is because they don't really mean it. It's much easier to back-peddle with the OW when they've blamed something more innocuous (like distance) rather than saying that they're married with a kid and they don't want to wreck their home sitch. It's also easier to keep the OW from contacting the BW if she doesn't know there is one. And some of it is just straight-up cowardice. They don't want their side-piece thinking they're a bad guy. Illicit affairs feed the ego, and part of the reason the WS engages in cheating at all is that they're getting a lift out of it.
That's assuming he told you the truth. You only have the word of a proved liar that she didn't actually know he was married. If so, the reason for telling you she didn't know is to keep you from being overtly hostile toward her. She's just another victim, you see. 
It's so tempting to believe the WS when you've just found out. We're still in shock. They sound so convincing. But they're practiced liars, who have sometimes been looking us in the eye and lying to our faces for years. I was astonished the first time I witnessed it, and even more so when I started putting the pieces together and remembering which lies went with which events.
It's NOT necessarily a hopeless situation though. But at this point of discovery, you've got to get this guy's respect and keep it. He doesn't get to lie to you anymore without consequence. He doesn't get to decide how much you're allowed to know anymore. And he damned sure doesn't get to say what he's willing to do and what he's not in terms of breaking up with his girlfriend. He's a married man. He's not supposed to have a girlfriend, right? It's absurd that they think they can set the tone for what's going to be tolerated after getting busted with their dicks still wet, and then think they can cry about how sorry they are, blame it on sex addiction, and cry to you about how they need help. This is YOUR life. This is your child's future. YOU decide what's good enough for you.
And that Facetime/texting nonsense would NOT be good enough for me. Why not tell him to get her on the phone and hand it to you? Tell her he's a married man with a child... and a history of seeing prostitutes. Tell her she's not the first and that he's already brought you home a scorching case of herpes from his last dalliance. Recommend she get tested. Then, tell her if she contacts you or your WH again that you'll be filing a restraining order, buh-bye. Say anything you want. It's not incumbent upon you to play nice in the sandbox with your husband's paramour.
After that, he closes his social media, changes his phone number, closes his email accounts, reroutes his bill-paying to a new email, and gives you passwords to every damned thing he owns. Hell, put him on a flip phone while you're at it. He goes to counseling and if diagnosed as a sex addict, he goes to meetings. His status as your husband is probational, because YOU DESERVE A BETTER MAN, and goddam it, if it's not him, it'll be someone else.
Sweetie, we all KNOW how hard it is to act tough when your heart is broken and your guts are jello. But if you don't get control of the situation, you'll be pushing uphill until you're finally so exhausted you just don't care anymore. It's kind of like dogs in a pack. You're alpha; he's a misbehaving beta. And you're going to tear his ass off if he doesn't capitulate completely to your will and show that belly. Not a very nice metaphor, but accurate enough.
This is not too much aggression. By everything that's holy you should be burning his shirts on the front lawn right now, so handing you that phone isn't too big of an ask. If he refuses, look him right in the eye and tell him 'that's okay, if he doesn't want you handling it, you'll go ask his mom to break up with his girlfriend for him.' No more Mrs. Nice Guy. Cheaters don't respect it, and his respect is so much more valuable right now than the tepid flavor of his "love". His "love" is cheap.
((big hugs)) You hang in there. Read everything you can. You got this.
