Here's another thing I thought of afterwards: If "Jen" has any normal sense of healthy boundaries, she will have zero interest in takng his daughter shopping, editing his resume, or meeting up with him for a beer. It sounds like she hasn't shown given him any encouragement on any of these ideas.

The facebook connection is inappropriate. I'm not that into social media, but my understanding is that you can put filters that will control who sees what. I'm flabbergasted at how open some people's facebook content is - to a point that even strikes me as unsafe and compromising the privacy of themselves and their friends. People with sense, IMHO, set up the filters so that the general public sees only posts of publicly available Net content - like pretty scenery or admirable quotations of published writers. (Personally, I don't let non-friends see anything on my wall.) Then a facebook user can set up distinctions between close friends and run-of-the mill friends. Photos showing who one is in a relationship with and photos of what one does with their nearest and dearest shouldn't be accessable to casual aquaintances, IMO. At this point, that's all your husband is to his former girlfriend. I think she's allowing him too much access to her private life. Some people may not know how to limit access, or be too lazy to set that up, or just not care who views their personal stuff. I would be a little suspicious of why she lets him see as much as he sees.

There is a very unhealthy trend going on of people wanting to keep peeking into the lives of their exes. This, IMO, is a neurotic use of facebook.