I stand corrected. It seems (looking at the Verbier website noted above) that you can ski "for free" at Chamonix.

From the website page (scroll down):

"Free skiing in Chamonix (except Aig. Midi, Gd Montets and Montenvers, 10 Euros)"

So in effect, with your Verbier pass you pay Euro 10 to ski at Chamonix.

As someone else mentioned, it might be the same in reverse (have not checked).

Verbier