Similar question being asked here and the answer is the same. Australian doctor, (non EU)
As Switzerland is not part of the EU you are still a non-EU in their eyes and would have difficulty in getting a work permit. Employers have to prove they can't find a Swiss/EU national to do the job. Outlined here: https://www.bfm.admin.ch/bfm/en/home...zulassung.html
As Island Monkey says, either your husband needs to move the whole family here (you can't do it as you're non-EU so you all have to come here as his dependents) or gain German citizenship - which would require giving up the US one iirc.
nqin, a G permit is not possible for a non-EU national as Zurich is not in one of the border zones. https://www.bfm.admin.ch/bfm/en/home...willigung.html
EU nationals with a G permit can work anywhere in Switzerland, but non-EU's can't.