@Padmail
I disagree that it's a husband problem. I agree that he might be a spineless twat, or that he might just want not to seem ungentlemanly (I think it's a bit of both).
I think the problem is predominantly her and her narcissistic nature continually needing attention.
Nope, you are still - (understandably) - looking to place the blame outside of your marriage by focusing on the woman.
If she's still seeing him, despite him saying he does not wish to, & he is unable to articulate his wishes, then the husband problem is down to spineless twattery.
Or, he has NOT told her that he doesn't wish to see her, in which case the husband problem is that he is fibbing to you to keep the peace, & has either avoided, or has no intention to, tell her where to get off.
If the situation were reversed, & DH was upset about an attention-seeking narcissistic man coming onto you, how would YOU deal with it? I imagine you'd make a clear declaration for the man to back off, & engage police if he refused to hear you.
If that IS what you would do in DH's position - why hasn't he?
See?
It's not an Other Person problem. It's a spouse problem.