Yet notice how you're not jumping to the WORST possible conclusion...(at least you didn't post them)
Here's MY sense of it...and of course I could very well be way off.
H IS more aware now of your insecurities about his female school chums. He doesn't know QUITE what to do about it.
So he's e-mailing her about the assignment (that's ASSuming it even WAS one of his ff classmates!!) when you come in.
In a panic he switches to the work...he IS actually working too. He knows this screen will be less likely to provoke worries/questions etc.
Sage...CJ has a real issue with me getting over-involved with certain students who have problems (eating disorders most of the time). I let myself get WAAAY too involved with one young lady and he was very resentful of the time I spent with or e-mailing her. Although he said not a thing at the time.
So THIS year, there's another student who I've kept at more of a "proffessor/student" level, I've NO intention of diving in so deep I endanger my own mental health again, nor my marriage.
Still, this student HAS shared things with me, HAS e-mailed me...and just the other day I was e-mailing her back when CJ walked up to the room. I SWITCHED the screen!! It was an impulse...I just didn't want to hear again how I needed to "be a professor" and nothing else.
I felt a bit guilty, still do.
Not sure if this helps any, but I think some similar mechanism might have been at play for your H there.