Probably not going to happen in today's world (at least in the 121 world), unless your family member is another airline pilot that has CASS status and can jumpseat.

There are a few occassions of where I've heard of a family team working together on the same flight (such as brothers or father/son or husband/wife).

I've had my wife in the cockpit of my corporate aircraft on a few occassions when the company has allowed me to take her along on a trip, and she's sat in the jumpseat of my airliner during the preflight and post flight phases (rode in back during the flight), but never had a family member up front of my 121 ride during flight.