I took Lydia as a companion on several quests and have had her pick up some booty off of defeated foes to carry back to Whiterun to sell. She is currently carrying steel plate armor (x6) and steel armor (x2). When I try to take either from her I get the following message: "You can't take your teammate's starting armor."
I had that happen once when I dumped a ton of items into a storage chest, then had her pickup the items. It made all clothing/armor in her inventory become starting armor and left me unable to take them from her. I'm not sure how I fixed it, but it took several hours before she went back to normal. Annekke did that to me once before too.
Never had the underwear issue though.