He (or "whoever") should be careful not to automatically assume that "looking insecurely" means she doesn't trust the husband and/or friend as far as any "affair type of stuff" goes... She may not be happy about whatever she is seeing when he and his friend are together, but that doesn't necessarily mean she feels that her own relationship with him is threatened by the friend.
Of course, there can be cultural differences with this type of situation; but generally, people choose their friends because they can relate to them in some way. Whether or not they can relate to their spouse the same way can be a whole other thing.
The husband (and again, "whoever else") should be careful not to do the demeaning thing of assuming that the wife is insecure about her own relationship with the husband.
If it's only that she "looks insecurely" when it comes to that one friend (rather than when it comes to all women and/or co-workers), the husband ought to ask his wife if, in fact, she feels insecure when he's with the friend (and in the meantime, not run the risk of flattering himself by assuming the "insecure look" is about "potential affair-type concerns").
If they have a decent relationship she'll be honest if she does feel insecure AND if she doesn't (and why) - and he'll respect whatever her reply to the question is and act accordingly.
It's often said that the road to hell is paved with good intentions. I tend to think something else that paves the road to"hell" is making up what or how people think by making guesses about how they appear to be "looking" or acting.
Also, though, she could well feel/be insecure if, say, the friend is also a co-worker in the same field as he; and while the last person he or the friend may ever be interested in may be the other there's the chance the wife feels insecure about, say, having little to contribute to the conversation.
In other words, even if she really is insecure it may well be more about something completely unrelated to her feeling threatened by the friend and/or her husband's relationship with that friend (at least as far as "romantic jealousy" is concerned).