Is he cheating??

So my husband and I work at Papa John's together, but I take the phone calls and he does the delivery. So on my 3rd day I see him talking to this girl with a beautiful shape and long hair name bria. Usually with everyone else, he introduces me to but not her. So they laughed and giggled and he has not said nothing to me.

He claimed she has a boyfriend whose a captain in the army and he's in the army. He didn't say anything to me until she left. Last night, he told me I could go through his phone, so I started to when he was playing with our puppy. As soon as I click the messages, I see good morning messages between them and him calling her baby before snatching the phone and getting mad. He said I should have let him know I was going to do that, but we're MARRIED.

What do you think is going on?

Edit: I woke up on Christmas eve morning and he was gone. These are his messages. He was rude to me on Christmas and want to say he's hurt because I want space.