Well I'm sure the insurance company would be more than happy to take your money. I think they ask what kind of permit you have, but you don't have to prove it. I would use comparis.ch to shop for the best deal (there are big differences in the prices you pay!).

Once you've found the insurance you want, and depending on how "modern" the company is, you should be able to have it taken care of very quickly.

Note that the right insurance for you might not be the same as the one for your husband, shop around carefully! Health insurance in this country is affected by your age and gender (fair), and where you live (not fair). Smoking is not considered by insurance companies for the basic insurance, meaning that non-smokers effectively subsidise the insurance premiums of the smokers. Pre-existing conditions cannot affect the minimum insurance which is required by law, and all companies have to take you for this. Optional insurances are another matter entirely!