Yes, it is priced per person. This is one of my only real complaints about
Adventures by Disney. I even mentioned it in detail on our survey after our recent Viva Italia trip.
It is frustrating to pay full price for a third person to sleep on a tiny cot crammed into an already small European hotel room. We are also a family of 3, and at 17, DD does not fit very well onto that little cot. The worst was in Florence, where the only place to put the cot was pressed up against the foot of the one bed. DH is tall, as is DD. So the poor girl spent two nights with her feet hanging off her "bed" while DH's feet were against her legs!
(I suppose, as the short one in the family, I could take the cot, but I'm not generous enough to do that. Teenagers sleep more easily than older ladies!

)
I am unwilling to pay the single supplement for her to stay in another room, but I do wish they'd discount her price even a little. She is definitely NOT getting the same level of experience as everyone else on the trip when it comes to the hotel rooms, yet is paying the same. Most of the other tour companies we have looked at do discount a third person in the room, so not sure why Disney is so set on this.
Incidentally, this has not been an issue on our two South American ABDs. Hotel rooms there are much larger, and set up for several people to stay in them. DD has always had her own bed - and sometimes a second bathroom - in the hotels, and even on the ship in the Galapagos, the sofa bed had a real mattress and was larger than the European cots.
This situation is why we are waitlisted for another South American
ABD, and are looking at the Asia one for after that, but will be doing Europe on our own from now on. We're renting a lovely apartment in Paris this summer with two beds and two baths!
ETA: Pens Fan, I don't mean to sound overly negative about this. It was only one small aggravation on what was otherwise a perfect trip. If your son is a typical teen boy, he could probably sleep just fine on the floor or a chair, so don't let my little rant turn you off from going on an ABD to Europe.
However, I do think that the only way Disney will consider changing this price policy is if enough of us triples question them about it. Unfortunately, I just think it's not that common for a group of 3 to take these Adventures.