Husband texting a female coworker and called her "girl"

I found out my husband has been texting a female co-worker back and forth quite often. He text her very early in the morning to check on her if she's awake. I found out quite by accident. I confronted my husband with this and he said that it was nothing. We ended up had a huge fight, he said he won't text her anymore, but after a while he started texting her again. Later he called her "girl", and then he deleted the message, he didn't want me to know it. Every time he text her, he always deleted the message.

Is it appropriate for my husband to text and called her "girl"?

I'm confused, and very upset. Please help!

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