The problem is that Parallels doesn't run windows programs in OSX, it runs Windows in parallel with OSX, and all the "integration" is smoke and mirrors. Coherence makes it look as if a Windows program is running right next to an OSX window, but that's a video trick and isn't what is happening under the hood. All the other tricks that make it look as if Windows programs are right there in the dock, etc., are routines executed in the Parallels monitor context, and only make it look as if the two are integrated. Windows programs don't run in OSX. Period. They run in Windows. Period.
You have a Mac, and a Windows computer running on the same box and sharing a keyboard and screen, but they are really two different computers, and will behave that way. You can access files over the internal network between systems, and that's the only mechanism available for sharing.
BTW, FWIW, I have not installed the coherence tool because it's just cycle consuming eye candy. It's a concept I very much DON'T love. Mac is Mac and Windows is Windows. They aren't the same and never will be.