The correct way to word this question is “How is your family?”
The reason is that while family refers to a group of people, it refers to the group of people as a single unit, or collection. Nouns like this are called collective nouns, and in American English, collective nouns take singular verbs. (In British English, many collective nouns can also take plural verbs.)
Here are some other collective nouns, shown in example sentences, all with singular verbs:
However, the collective noun police is an exception. It takes a plural verb, as in this example:
The police are questioning the suspect.
I hope this helps.