Hello GrandEntrance, a warm welcome to the site.
I think it is very difficult to watch out for something to not happen vs waiting for something to happen, as Tim has said is so true, perhaps your partner feels it's much safer to talk with someone he doesn't know rather than with an actual person, face to face, in the first case it can be ended easily, while in the next, it may not be easy to finish talking with them and one of them may want to continue causing disruption to your relationship/marriage.
I'm not saying that it's alright to do this, the concern is, when you both go out with the baby, everytime he talks to a female, just like you talking to another male, you will feel as though that maybe the person he's talking to online is present, which maybe far from the truth.
The way he's responded to you, I believe he feels guilty and wants to rebuild the trust you had before, and what reaction would happen if you caught him going through your phone, sorry, but try and believe in each other, this may have only been a one occasion.
Best wishes.
Geoff.