In a talks with Game Informer Microsoft detailed how DLC for Xbox 360 games will work with the new backward compatibility feature on Xbox One. DLC that you previously purchased will be available but you will not be able to purchase new DLC via the Xbox Store on your Xbox One.
“Right now, Backward Compatibility does not emulate the Xbox 360 store and new Xbox 360 games can be purchased on your Xbox 360 or via Xbox.com,” a Microsoft representative states. Game Informer also confirmed that all DLC will be supported and automatically downloaded to you Xbox One along with supported games.
If you already own the DLC then everything should be set and ready to go once the backward compatibility feature goes live on November 12. “We will support both digital and disc-based entitlements for Xbox 360 games running on Xbox One”, says Microsoft. Please note that if you want to purchase new content add-ons and DLC then you can do so via Xbox.com or on your Xbox 360.
Source: Game Informer