Actually, I'd say "My brother is in the Navy, assigned to a submarine."
If he's just "working" there it doesn't sound like he's part of the crew.
However, if you want to work on the "onboard" thing, then say something like "The last time they were in home port, I was able to visit him onboard." (or on-board - both are acceptable.)
(I don't see much difference between onboard, on-board, and aboard.)