Hello....RCCL has two formal nights in the main dining room. I hate to wear a jacket myself, however, a jacket is required for both formal nights. That does not mean your husband has to wear a tuxedo. He can wear a dark suit, or dark dress slacks and a dark sportcoat will do. Shorts are not allowed in the dining room any night. For lunch, it's OK. They might not say anything if he wears shorts on other dinner nights besides the formal nights, but I beleive that not to be the case. I have worn dockers and a polo shirt for dinner and that is fine. On dinner nights besides formal, smart casual is fine, but no shorts. If you decide not to dress up on formal night, you always have the option of dining in the Windjammer Cafe where you can where shorts, tee shirts, etc.
Hope this helps a bit. We are going on the Adventure in October. Cannot wait.