Husbands teacher- friend?

My husband's college teacher is still in touch with him after almost 7 years of passing college.. Thts not my problem? My problem is that they keep messaging each other even late night and early morning say at 6am.. She is hardly 7-8 years older to him.. When I confronted him he said she is just his teacher and I shouldn't even think about doubting him with her...once I even caught them chatting on the phone at 11 in the night, and when I asked who it was he lied that it was his colleague from the hospital.. Why does he want to lie?? I'm married for just 5 months and am confused as to what to do about this...I can't share this with anyone..Theonly comforting thing is she stays in a different city, but still isn't this a kind of cheating... Also my husband has a weird habit of flirting with girlfriends on fb.. He keeps staring at other girls when we are out together..I know this sounds all bad, but he is a very nice guy...he treats me well and respects and loves me a Lott...but all this things are killing me..I tend to get distracted at work thinking about all this..please help how to deal with this...is this the case with most guys, should I just ignore this.??