Actually, very very seldom. If (not when) people start asking me question like that, I would ask back: "You FBI?"
As a matter of fact, family information is usually voluntarily revealed, not asked, unless for certain reason, and even that, very specific, not generally.
If you want to get to know a person better, there is only one way: lots of exchanging information thru chatting. Family particulars, obviously, are included. You accumulate this scattered information to form the big picture about the family.