That's not a very thorough answer, unfortunately.
Was the content purchased using his account or your's?
Just downloading the dlc to his xbox will not allow him to use it if it was bought using your profile.
For him to use it, you'd have to do something called a "license transfer" to update the licenses on his xbox before downloading the map.
This, however, means that you would always have to be signed in online on your xbox in order to play any content attached to your profile. That might not be a problem, but thought I should warn you.
Here's some further reading on digital rights and the process: support.xbox.com/.../download-content