How long would you say it takes to cross from Chamonix to Aosta? Would continuing to Milan in the same day is that possible/recommended?
Do you plan to drive thru the Mont Blanc tunnel -- or do you mean to go up to the Aguille Du Midi -- then continue on to Hellbronner?
If you intend to drive thru the Mont Blanc Tunnel it takes about an hour to drive straight from Chamonix to Aosta. From Chamonix to Milan would be close to 3 hours. If you are asking about going up and over Mont Blanc via the lifts and then trying to use public transportation once you get to Italy then it will take longer. Someone else may be able to speak to that.
I am wondering about using the lifts and public transportation.
I tried to do the Chamonix -Aosta via lifts July 2009. It snowed so hard we could not use the lifts for days. So plan a few hrs to Aosta via lifts if weather OK. otherwise you can bus it from Chamonix to Aosta. I have not completed the Aosta to Milan leg but it is a fair distance with transfers so I think it may be difficult to do in one day. Time of yr for freq. transport schedules is imp. in this area.Hopefully your are thinking summer.
the beginning of september.