No "free" passes my friend. Sorry, not here. You and your immediate family have unlimited staff travel privileges on CX, but you are charged for every ticket you use. Regional travel is reasonable, but charges on longhaul are pretty high once you factor in the fuel surcharge.
For example, LAX to HKG in economy (y class) will run you almost $200 USD one way. Your family does get to travel on the jumpseat if needed (kids 12yrs or older) which is kind of cool.
You are also allowed one travel companion who gets 12 one way staff tickets per year, but I think this is only for single people. Your parents are also allowed 12 one way tickets each.