There are plenty of private International schools between Geneva and Lausanne, where English is the mother tongue, so you could try those for teaching positions.
You can definitely get by without French, from an employment front for your husband, there are lots of International companies and International organisations where English is the working language. Economy is not doing well at the moment, so job hunting may be difficult. For you daily life, you will find plumbers, electricians, hairdressers, beauticians, doctors, dentists etc who all speak English, there is a good English speaking community.
Property prices are eyewatering,and most people rent for their whole life. As an Eu citizen (uk for the moment) there is a bilateral agreement to allow you live and work in Switzerland, a lot of people live in France and work in Switzerland.
The swiss Education system is very rigid, but if you did put your child into a local school, they will be bilingual in a few months. Students are 'streamed' very early as of 11 or 12, into 'apprentisage' or 'third level. If you found a teaching job in a private International school, chances are it will come with free education for your children. I think you would need to be fluent french to be hired by a local school.
There is no free health care, and health insurance is huge, most employers will pay, or at least contribute towards the cost.
As someone above mentioned, avoid living in Geneva and look in Vaud (La Cote), anywhere from Mies to Lausanne.
It is a wonderful place to live, easy access to rest of Europe and lots of outdoor activities.