Continental Airlines Presidential PlusSM primary Cardmembers get their first and second checked bags free. Other Continental Airlines Chase primary credit Cardmembers get their first checked bag free.
it looks like it won't work for the whole family only the primary cardholder
It works for anyone on the primary cardholders reservation automatically.
It also works for non-primary cardholders and their whole reservation, but an airport agent has to override that manually.
CO/UA elites also get 2-3 free bags for them and everyone on their entire reservation.
The general rule is that everyone on the same res has the same policy as the most privileged traveler for everything except for upgrades.
For upgrades the opposite rule is true-it follows the least privileged traveler. Which is why you should book everyone together and then split the elites off of the reservation...