Instead of focusing on your husband's co-worker and expecting HER to do the right thing, maybe you should have focused on your HUSBAND and expected HIM to do the right thing. What did you expect to get from your original communication from her? You told her that you thought her posts could be viewed as inappropriate and you were concerned as to how "they might come off". Why would you turn to her first regarding how their interactions might "come off" to others?
This is REALLY passive-aggressive behavior, IMO. Why didn't you contact your husband first and insist that he delete her as a contact? Why did you contact HER and ask that SHE fix things the way you want/need for your marriage?
I agree and disagree. Sometimes taking matters into your own hands isn't such a bad thing. But yes, she should have spoken to hubby first, with an eye towards rectifying it. She did, technically, and he blew her off, so she followed the logical next step, IMO.
I had this type of thing pop up a few years ago, wherein a male co-worker of my wife's would do similar things on her Facebook. Nothing outrageous, but clearly with an agenda (no matter how small).
I spoke to her first, and received much the same response as OP's husband gave her. Which is to be expected, really. I trusted my wife (still do), and I understand the awkwardness of her (or OP's husband) having to have a "chat" with the offending party.
It did continue, but my wife did not reply or respond in any way that would give this guy any thoughts that he had a chance or anything. Fine by me.
Until he posted a rather inappropriate meme photo and tagged her in it. (something to do with wives and blowjobs, if I recall).
She agreed that was not appropriate, and deleted it, but said nothing to him (that I know of) - so I did. Sent him a message, and politely told him that was out of bounds, not just for the obvious reasons, but also that our teenage son is on Facebook and likely would have seen that picture.
He didn't respond to me, but instead sent her a message, saying I contacted him about this picture, that he was sorry (that he was drunk when he posted it, lol!!!) and it won't happen again. She never responded to him, at least through Facebook (and likely not in person, either).
I'm with OP on this one, more or less. You can handle these things any number of ways, and they're all likely to bite you in the ass, somehow.
But sometimes being passive and expecting your SO to handle it isn't reasonable. If I were in OP's husband's shoes, it would be awkward for me to tell my co-worker to knock it off. I still would, but not everybody has the where-with-all to do so. I believe my wife is like that, as well. She has to work with this guy, doesn't want any office drama, etc. But I trust her, and her general lack of responses to this guy is enough for me. If he wants to keep wasting his time, that's his prerogative. And if he's dumb enough to keep barking up the wrong tree, well that's on him, as well. Meh.