Maybe I can still contribute something about Switzerland, I have dealt with it very intensively, after my studies I almost signed two contracts there:
A salary of about 6500,- SFR * 13 months is therefore quite normal in Switzerland - depending on the taxes (different depending on the canton), it should be about 5000,- € net. The cost of living is much higher, but usually does not completely eat up the salary increase.
BUT:
If your husband "only" gets 4,000,- € net in Switzerland, that is quite tight - if you then also want to become so-called cross-border commuters, your net income will be significantly lower again, since you have to pay certain contributions in Germany - so it is by far no longer 4000,- €. That means: living near the border is cheaper (groceries), but the total contributions are much higher - so it’s really not worth it - my best friend now lives there on site and has exchanged information down to the last detail with his tax advisor and the authorities.