The only massages that include the private balcony and hot tub are the Spa Villa packages. I'm pretty sure a regular couples massage would not include the spa villa experience. But it would be in a nice treatment room.
DisneyNDecember, I have had lots of massages and as much as I love my son, ain't no way I would sign up for a couples massage with my DS. You have to disrobe, at least partly and no way am I doing that with my son there.
What I suggest is to book a massage for you and him separately but at the same time frame. That way you can go to the spa together, then split to the separate dressing areas. I treated my DS to a massage when he was a very young adult on the cruise and he loved it. I have booked concurrent treatments for myself and family members many times. We trot down to the spa together, and come out together looking like very happy, limp dishcloths.
I have done a Spa Villa experience with my DD, and enjoyed it though it took a bit more effort to disrobe discreetly with her there.
For those that have never had a massage, when you arrive early (at least 15 min before your appointment time) for your app't, they will ask you to fill out a health history. Then you will be taken to the women's or men's dressing/locker room respectively where you will get out of your clothes and put on a spa robe and slippers. I kept my own flip flops on because they were more comfy than the spa slippers. There is a small relaxation area in the dressing rooms to wait until your therapist comes to get you. Once in the treatment room, you will be shown where to hang your robe, and given instructions on whether to start face down on the table (generally they start face down first with massage), and to cover yourself with the linens on the table. The therapist will step out of the room and give you privacy to do all that. They will knock before re-entering the room to make sure they respect your privacy.
If you are shy, you can leave on your underwear, though I don't recommend women keep on their um, "upper" undergarment. You would not enjoy the massage as much IMO. They will only uncover the part of your body they are working on at that time so you will be covered for the most part, most of your treatment.
To get the most enjoyment out of your massage, be assertive to let the therapist know how much pressure you like, and if you are at all uncomfortable at any time let them know. If you're cold, let them know. If you're too warm, let them know. If you are extra shy about your body, let them know and they will make sure to keep you more covered. Remember, YOU are the consumer and the therapist can't customize it to your personal needs if you don't let them know. 
ENJOY!!! Getting a great spa treatment is one of my very favorite splurges! Especially on a cruise. 
Are these offered in those rooms with the balcony and hot tub?
Generally speaking, couples' massages (a la Disney) focus primarily on the main task at hand--the massage. The music is some light & airy, New Wave-ish style piffle, and the atmosphere is one of relaxation not titillation. I'm sure you'll be fine.
