Is texting cheating?

I recently discovered that my husband of three years was texting a girl back and forth and he met her for lunch one day. Since then he swears he broke it off and tell me that since I had our second baby he just felt ignored and enjoyed the attention and flattery. He swears nothing physical happened but I tell him he may as well have screwed the girl because the betrayal feels the same. She knew he was married and she still played along and pursued him. I want to forgive him but I can't get those messages out of my head. What do you ladies think?