You can enter unavailable dates (or update shift preferences or other contact information) for an entire family at one time by opening up the family in the Families pane and adding the can't serve time in the Edit Family dialog, as opposed to adding the unavailable time to the profile of an individual volunteer within the family.

If no Families pane appears, first go to Edit and select Show all panes. Click on the Families pane, then open up the family to which you'd like to add the can't serve time, add the time, and then close the Edit Family dialog. The can't serve time will now apply to and be visible in each family members' profile.