well, they always say that communication is the key when it comes to relationships... if you have a hard boundary about this sort of thing, then you and she need to discuss it to see if she can respect that boundary.
She may be doing it for the reason you state, but then again she may be the type that posts all sorts of happy stuff on their Facebook page, to share with the world. Either way, if it bothers you, you need to talk with her about it. Note that I said "her" and not "him" - if you have an issue with her behaviour don't put him in the middle of it - it puts him in an awkward position and may well dilute the message and the reply.
I wouldn't put it as an ultimatum ("Stop posting all that Facebook stuff when you are with him!") but instead talk to her about how what she is doing makes you feel (uncomfortable, sad, whatever you are feeling) and that for this reason you'd like to see if you can come to some understanding with her.
Does that help any?
"Listen, or your tongue will make you deaf." - Native American Proverb