Her mom is Bebe Buell a 70's supermodel that was in Playboy at some point back then. Liv is Tyler's daughter from an affair Bebe had with him while she was in a relationship with Todd Rundgren. In fact, Liv's birth certificate listed Rundgren as her father and her name was originally Liv Rundgren. Pics I've seen of Steven Tyler's other kids all have his .er... smile. Liv got lucky.
A few vintage pics of Bebe Buell are at
http://www.playboy.com/playmates/per.../mystory1.html