In "Romeo and Juliet," reference is made to Benvolio being of "the house of Montague." Does this mean he lives with Romeo and his family?

Good question. The answer is no (or at least, 'not necessarily'), actually - though you're on the right lines. The two 'houses' referred to at the start of the play, and throughout, are those of Capulet and Montague. It basically and simply just means 'family'. Benvolio is the 'nephew' of Lord Montague (and therefore Romeo's cousin) and like the rest of the Montague boys, is from the same family - though it's a very extended family.

Same thing is true of the Capulets: Tybalt, Lord C, Lady C, Juliet etc. etc. are all of the same family but do not, it seems all have to live in the same house (it seems that Tybalt and Cousin Capulet, for example, don't live with the Juliet, Lord Capulet and Lady Capulet).

So 'house' just means 'extended family'.

There are three exceptions in the play it's worth knowing about, who aren't from either house. They are the prince, who's obviously from the royal family of Verona, and then his two 'kinsmen' (family members): Mercutio and Paris. Mercutio, though he hangs out with them, is not a Montague.

Hope it helps!