Swiss Pass covers Chamonix? Pretty sure that's in France.
It is, and it does. The Swiss pass covers Martigny to Chamonix, but the Half Fare Card does not. The Swiss Pass covers a few other cross-border lines as well, such as Brig - Domodossola - Locarno.
See the official Swiss Pass map here: https://www.sbb.ch/content/dam/sbb/de/infotexte/uebersichtskarte-sts.pdf
@rjrietkerk, you can use this map for planning- All the red lines are rail lines, and every line has at least one train per hour.
Are you flying into and out of Geneva? If so, Chamonix to Geneva airport is quickest by direct (French) bus. Multiple companies offering this route, just google.
And a car is useless in Geneva and Bern and of limited use in Lauterbrunnen. Lauterbrunnen is the end of the road, and you will be wanting to go up the mountains, that is past Lauterbrunnen, the only road is back down the valley out of the mountains.
You can't even drive to Zermatt.
P.S. Swiss Pass prices and purchase is here: https://www.sbb.ch/en/leisure-holidays/travel-in-switzerland/international-guests/swiss-travel-pass.html
Swiss Travel Pass 3 days CHF 225
Swiss Travel Pass 4 days CHF 270
Swiss Travel Pass 8 days CHF 398
Swiss Travel Pass 15 days CHF 485
Swiss Travel Pass Flex 3 days in 1 month CHF 259
Swiss Travel Pass Flex 4 days in 1 month CHF 310
Swiss Travel Pass Flex 8 days in 1 month CHF 445
Swiss Travel Pass Flex 15 days in 1 month CHF 532