Trebbiano is a name applied to a confusing group of white wine grape varieties originating in Italy. Current DNA research suggests that many are distinct varieties with distant or unproven relationships to other grapes in the group. Hence "family" is not the best way to describe them.
They do share some traits; the most basic one being that they are all white varieties. Bunches tend to be long and large, the berries are usually late ripening, and the vines are vigorous and adaptable to a range of terroirs.