If you want to write cross platform applications use Qt. End of story, it's the only extremely well supported cross platform GUI framework out there. If you are looking for a smaller framework you can try WxWidgets, but I would stay away from GTK. GTK has been getting less and less support since version 2. Version 3 is only Mac and Linux and the Mac version is terrible, there is a "custom" Windows version by some french guy, but it's just that, not community supported.
You could also take a look at Juce, depending on what you need to do with it.
But, if you don't mind large binaries you could easily embed a chromium or awesomium layer as your frontend and do your frontend in html/css/javascript and use JavaScript to communicate with your backend.
As people as said, the best idea would be to write one backend and three or two frontends. That will give you the best experience on all three platforms, and the native GUI look, something that on Mac Qt still suffers with.
You could also take a look at Juce, depending on what you need to do with it.
But, if you don't mind large binaries you could easily embed a chromium or awesomium layer as your frontend and do your frontend in html/css/javascript and use JavaScript to communicate with your backend.
As people as said, the best idea would be to write one backend and three or two frontends. That will give you the best experience on all three platforms, and the native GUI look, something that on Mac Qt still suffers with.