What would you do is your estranged female neighbor constantly spoke to your fiance in front of you?

Okay, here's my issue. I have a neighbor that lives 2 floors above me. She always speaks to my fianc� and even joked with him once when I was around but didn't say a word to me. I personally take this as an insult because she has a boyfriend that lives with her. When she speaks to him and only him with out him speaking to her I feel she's making a point to flirt. I am not jealous or anything but I can be at times and the only reason that I am not is because she's not attractive in the least. What I dislike is that I feel like she's disrespecting me. My fianc� said he sees my point and if the roles were reversed he's say something. I haven't said anything because I feel if he knows this than he shouldn't speak. I don't know what to say to stop this but he feels it's innocent. However, I am more than sure if I went out of my way to speak to a man (neighbor) on a regular he would think it was promiscuous behavior so I don't understand why he doesn't recognize this in her. Am I tripping?