My husband also works in law enforcement. I understand where you are comming from. You say she has been doing this for a year, so heres 2 options. You hubby either hasnt been firm enough with her and he needs to, or there is something going on between them.
If I were you next time you see her post something, send her a messaage back yourself and tell her that you dont agree with her acting this way towards a married man and that you are asking her to stop. Depending on her reaction and what she says, might let you into the actual situation a little more.
Also, if given a chance, have your hubby tell her to stop in front of you. Have him point out to her that he is married and that it is inapropriate what shes doing. Also, have him tell her if she doesnt stop that he will go above her head.
Id also ask him to unfriend her on FB. This will solve alot of the issue.
This really sucks, but I'm not sure how long you have been married to a PO, but its a whole different world. I grew up a cops child, I worked in the sherriffs office as a civilian for 5 yrs. My hubby was not PO when we married, he did this after. Many of my friends keep asking him to set them up and his reply is, Cops are pigs, I will not set anyone up with another.
This women has no scrupples and since your hubby cant seem to put a stop to it, you need to. DO not go to her boss yourself, this can cause problems for your hubby.
Good luck, and from one cop wife to another, if you ever need to talk, please message me, ill give you my email or phone #.