Day of the Triffids

While I wasn't looking, some kind of freaky creeper vine crawled up one of my trees and all over my poor rosebushes. I pulled it off of the tree (well, mostly, sort of), but rosebushes bite you when you try to do that. Anybody have any suggestions (other than "wear thick gloves")? Is there some kind of herbicide that kills freaky creeper plants but not roses?

Yes, I know. My ignorance is utterly appalling. I am merely an indifferent housekeeper, but I am a terrible gardener. Really, I shouldn't even have plants, and I certainly wouldn't have roses if they hadn't come with the house. If I ever have the cash, I'd like to just xeriscape the whole damn yard. I approve of xeriscaping, both environmentally and aesthetically, but most importantly, once you've covered a yard with gravel and cactus, you can then effectively ignore it.