If it's making you feel bad then it's not ridiculous. Have you talked to him about it? If so, what was his response?
If he is concerned about the image of his family, it is possible he wouldn't want to jeopardize his family. Even if he's not actually cheating, the staring, and having her staring back is still disrespectful and he should know that. It's hard to know how to act when someone shows attraction towards you, even if its out of line, there's still that bit of fascination about the unknown, but he realize that if you noticed it, then others may notice as well. Kids can be cruel and if this were to get around the school there's no telling how they might treat your daughter.
The best you can do is trust him until he shows he can't be trusted....you can't accuse him of something he hasn't done, but you can let him know that you're aware of the looks whether he wants to admit to them or not and that he has to understand that by looking at her he's giving her ideas or at the very least the idea that he might be interested even if he's not.
Getting to know her better. I'm not sure what you mean by that, but I would never bring her to your home or near your family. It's true that you should keep your friends close but your enemies closer, but be careful of making friends with her just for this reason. Being friends with you could give her the perfect excuse to contact your husband.
I welcome your thoughts, let me know if you want to talk more
You could go crazy trying to figure out people you know, not to mention people you don't know. We never really know what's in the heart of another person. You could look like someone she used to know or someone in her family....or he could look like someone she knows or used to date, so she has developed an interest in you, him or both. This could certainly be a case of he being fascinated with you or feeling in competition with you, and of course the first thing to look at would be your husband, and then you children. You might be surprised, she may try on her own to make friends with you.
Talk to him, no hysterics, and bring up what I said earlier about others noticing that they are looking at one another and how that could impact your daughter.
I'm here if you want to talk more.