when I found the original messages I saw that he told her he didn't love me.
Why would you stay with a man who doesn't love you? I know many people in affairs lie to the OW/OM in many different ways.
They lie to justify their behaviour...because if he said he does love you, that would make him look like the bad guy, who cheats even when he loves his wife.
That would let her know, she'll receive the same if he leaves you for her.
Now he's telling her he only stayed for the baby, that he doesn't love you and you live like housemates.
Rather than get top stressed right now, as it's no good for the baby....remind him of when he said he doesn't love you to her, let him know he is free to leave and that you would like an amicable coparent relationship with him.
Stop fighting for the marriage that he's not committed to. Change your mindset about this, because having to police your spouse is no way to live.
At the end of the day, if you love someone, you want them to be happy and if he can't be happy with you, to the point he keeps on cheating, then cut him loose and build a brighter future for yourself.
Google the infidelity 180 and implement the points that you can. It's to build you up and gain confidence.