I used to be able to use Super+Mouse1 both to move a window and to raise the window on click. When I upgraded to 12.04 gnome-panel, it lost this functionality and I was forced to map F1 to raise a window. Now I am auditing Unity. I have disabled click-to-raise and auto-raise behavior as I would rather have control over which windows are raised when.
I am not aware of a way to map the mouse thusly, but I would be happy to hear that it is possible.
Best Answer
I have more or less solved the problem. It's not ideal but it works. In CompizConfig Settings, General Options -> Key Bindings, there are two settings for "Raise Window", mouse and keyboard controls. I set the mouse control to Super+Button1, which does not conflict with Alt+Button1 in the "Move Window" options. I also set "Lower Window" to Super+Button2, for orthogonal operating with clicking the title bar.
Although this does not combine raise+lower like I am used to, it allows me to access raise/lower while using the mouse, so it's good enough for my purposes.