My girlfriend and a married man often send text messages and make phone calls. Is it normal?

What you think is right. There won't be any real bosom friends between the opposite sex.

First of all, you should have confidence in your girlfriend, be more careful and make yourself better than that man.

Secondly, we must not be narrow-minded. Sometimes it's not that serious, but it can be caused by complaints.

Finally, it's best not to go to that man, otherwise it will easily lead to misunderstanding (his family misunderstanding, your misunderstanding). If it is irreversible, think rationally about your relationship.