I had been having the devil's time figuring out how to accomplish an excursion from Couermayeur in Italy to Chamonix in France via cable cars, and back to Coeurmayeur via bus as a round trip.
It is not well explained in any book I have that covers Italy, though Rick may cover it in a French/Swiss Alps program or book.
Here's what I've learned. The French side is run by one company, from Chamonix to Punta Helbronner, which is the border crossing. An Italian company runs the cars from Punta H down to Coeurmayeur in Valle D'Aosta. The Italian bus company runs the bus in the Mont Blanc tunnel.
No one sells a ticket beyond their operating area. So to do the full round trip, it's a one way to Punta H from both companies, plus a bus ticket from SAVDA. What we've opted for is a round trip from VdA to Punta H from the Monte Bianco company, then a round trip covering Punta H to Aguile du Midi on the French side. No tunnel, which I'm told isn't that interesting.
Additional note: The French do not sell the Aguille du Mini Panoramic cable car over the Internet or in advance. This is what they call the Punta Helbronner to Aguille du Midi cable car. It is only available at the cash office on site.