The captain was in his underwear because his armor was destroyed. Even though it was funny, It became a pet peeve of mine quickly.
Hey, just be glad you weren't using a nvde body replacer
Now that would be embarassing.
But back on the subject at hand. It's important to keep in mind that companions weren't an important part of Oblivion. In fact, you couldn't even have a companion on a regular basis unless you count summoning spells, you just had NPCs traveling with you for some quests, so it's no surprise that you couldn't give them items. In Skyrim, though, since Bethesda is including companions as a feature of the game, I expect we'll have a companion share option, much like we had in Fallout 3 and New Vegas, so that you can give companions equipment and should also be able to repair their items, that should fix the issue.