They. Technically, either should work, but "they" is the more common usage. Although the family would seem to be a singular group, using "it" makes it sound like an object....or at least a group that functions like a single body. In reality, the family is composed of many individual thinking people whom we think of as "they".
In some contexts, it might be your intention to single the family out as a single entity, perhaps like a powerful family dynasty. In that case, "it" might more appropriately convey this meaning. In most cases however, family is referred to as "they".