That's very difficult to make it truly transparent without using an interface which XNA does not support due to its D3D version, but there are workarounds that sort of get what you want.
You can get similar appearance by hooking into the Windows API and grabbing an image of the last rendered "client area" of the window (the desktop is just a special window). In your case you could get all other windows that yours was overlapping, grab the client areas, clip them using your relative position/size, then mix them together in a shader. Warning: This could be performance-intensive on update, depending on how many windows you had "beneath" your own. I suggest hooking into updates from the window so you're only capturing when there's a change or when your window moves, etc.
Check out these in the Windows API:
[DllImport("user32.dll")]
public static extern bool GetWindowRect(IntPtr hWnd, out RECT lpRect);
[DllImport("user32.dll")]
public static extern bool PrintWindow(IntPtr hWnd, IntPtr hdcBlt, int nFlags);
Be aware that this will not help give your window border any faked transparency though, only your render area.
Also see: Transparent window layer that is click-through and always stays on top
You might be able to use some of the information in that thread as well.