Using Steam's Family Sharing feature, can you share DLC as well as games?
Yes, you can share DLC with Steam Family Sharing.
However, DLC will not be shared if the "guest" (as opposed to the lender) also owns the game:
Who owns and can access the DLC and in-game content associated with a shared title?
A guest will have access to the lender's DLC, but only if the guest doesn't also own the base game. Guests may not purchase DLC for a base game they don't own. Any player may purchase, trade, earn, or otherwise acquire in-game content while playing a game, but in-game items cannot be shared between accounts. These items remain the property of the account that purchased or acquired them, whether borrowing or lending the base game.