weird rose AND cherry bush

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.

They don't graft cherries onto roses, so I suspect if you look closely you'll find you have two plants growing very closely together or something along those lines. Or the rose died and now there's just a cherry tree there. There are grafted roses (one rose grafted onto another type of rose) and grafted cherries (grafted onto another Prunus species) but you won't find cherries & roses grafted onto each other.

The Leaves are from the same species no matter what plant it came from, either Rose or Cherry, one leaf is more mature than the other thats the only difference other than the blackspot that would tilt it to-wards the Rose.
As Ecrane has already said you get Roses Grafted onto other Rose stock and likewise the same with Cherries, the Norm is for the breeders to use a strong or wilder trunk or branch depending on the kind of either,then they select buds or young side shoots and make slits into the selected trunk /branch, tape these to keep in place and the trunk / branch then takes on the new buds and they in turn grow on to produce the same flowers as the parent plant the buds / side shoots were removed from, this is how the breeders produce weeping / standard trees. I have given simplistic info as to how they do grafting, it is ofcourse much more difficult and many years to learn how to achieve this technique.

What I would suggest what you do is scrape away some soil from around the bottom of the main stem and see IF you can find a wound where there has been a graft at the base, of the root stock as that spot is where they would normally do a graft to create a climbing rose which would indicate why you have such long stems on some branches, it sound like a climbing Rose.
There are as many types of climbing rose as there are hot dinners and the same for the size, colour of flowers, the type of Rose that could be looked at as similar to cherry blossom would be the class of rose known as a Ramblers, these have flowers that do look very like Cherry blossom and they come in flowers coloured deep pink, red, yellow, white etc, cherry blossom comes in shades the same, as you said there are long Branches 12feet tall It points to me like you have a climbing rose or Rambler. I'm sure you could get a picture of the shrub tree even at this time of year, doing that would help identify from the growth / branches etc.
Meanwhile just enjoy, if you do have a cherry, you would have seen signs of tiny fruits by now, Good luck. WeeNel.

Don't roses have compound leaves?

There are such a variety of different Roses today that there are so many different leaf shapes and colours even stems , some people are selecting a certain Rose because of the branches that have red colours or bronze leaf.
I really don't know IF all Roses have compound leaves or not but if you look closely at the pictures sent in, they have identical veins, and leaf structure, one leaf is immature therefore not the identical shape as the other and it also shows sign of disease, common to Rose foliage but, would like a second opinion, a picture of the whole plant would be better as would more info from the owner, I am not an expert in any way but have grown both Roses and Cherry for many years, but as mentioned, there are hundreds of Roses as there are Cherries.
Hope the owner puts us out of our misery eh!!!. good luck WeeNel.

The leaf spots shown here are typical of cherries, crabapples, and many other things in the rose family, most of them tend to be susceptible to leaf spot diseases. We'd have to see more of the plant to know for sure what it is--to me they look more like tree leaves vs rose leaves but it's hard to say without a bit more to go on.