Advice needed! Help!

Ok so here's a short background story. My husband is finishing up becoming a teacher ( super proud) but he is in this group and he is the person to seek for help. Jump ahead,he had a class with this girl previously and now that they are student teaching ( he says she is in another school) but they text everyday and he will text her before me in the morning when he is in school and when he does text me it's a quick hi and I'm busy gotta go. He doesn't know that I know he talks to her that frequently. I've spoke to him about it right when the texting started and he said its all work related, from what I've seen he is telling the truth. But today I saw that he googled imaged her idk what to think of that. Not to mention porn stars where before and after in the history. I'm I going crazy or does this look bad!