Would you call this cheating?

In February, while my husband was away doing some extensive military training, I caught him messaging and mildly flirting with another girl who was there at the base. Yes I was snooping on his facebook. I didn't trust him because of a similar situation from a couple years before. In both situations, nothing physical happened, but it was a huge breach of trust. He messaged her for about 5 hours, asking her to come hang out with his group that weekend. He then deleted the messages, asked for her number, then deleted that message plus all messages from another female (who he wasn't flirting with). I thought about it for a week while constantly checking our phone records. He texted her all day, first thing in the morning and at night, sometimes a few times before getting back to me. I was distant and he hardly noticed. I confronted him and he lied - he didn't know I could see phone records. I told him that and he said I'm so sorry blah blah blah. I said send me the messages. He deleted half of them and screenshot the rest, not knowing I could see exactly when and how many messages. He says there wasn't anything in the deleted messages that was worse than the others but OBVIOUSLY that's not true because why would you delete them?

Anyway, this was months ago and I feel like some progress has been made but I think about it all the time and I'm always on edge and insecure about other females. I used to pride myself on not being that way. :/ I often feel like he doesn't care. Not always, but often. For instance, he forgot to say happy birthday until he was at work... it's the little things...

Opinions? Cheating or no? Does a label even matter? I miss the trust.