Beginner Gardening: weird rose AND cherry bush, 1 by ExStock

ExStock wrote:
About 3 years ago, I bought my first house. (Yay, me!) In the back yard, there was a lovely thorn-less rose bush with big red roses all over it. Being completely new to tending roses, I didn't really do anything to take care of it, and the next year, there were no blossoms. I looked into it a bit, did a bit of pruning and fertilizing, and lots of bug spraying due to a rose chafer attack, and waited for blossoms-- no blossoms. Then, finally, this spring, there were blossoms...

...Cherry blossoms. Several branches on the ~8 foot tall rose bush were covered with cherry blossoms. Assuming that a cherry tree had been grafted onto the rose bush, I first looked for some obvious signs of grafting on the branches/trunk/whatever you call it in a large bush, and found none, nor was there any obvious-to-a-newbie difference in the bark anywhere. Next, I looked at the leaves to try to figure out which parts were cherry tree and which parts were rose bush, but that confused me even more, because every branch all over the bush had two different types of leaves on it. (See image; these leaves were side by side on the same branch.) There's no discernible difference between any parts of the bush, apart from the fact that it somehow it's both a rose bush and a cherry tree. (And there's no other bushes in that part of the yard, so it's not like I just forgot which bush was the rose bush and which was the cherry tree. =} ) Sadly, I have no pictures of the bush with either type of bloom, and haven't been able to identify the type of rose I saw yet, because it's hard to remember enough detail after 3 years other than "the flowers were red and looked like roses".

I'm curious about what's going on, but the main reason I'm posting here is because I have no idea how to take care of this thing! Do I prune it as if it were a cherry tree, or as if it were a rose bush? (After the cherry blossom incident this spring, I didn't prune it at all, and it's now a very leggy 12 foot tall mess.) How do I fertilize it? ...and so on.