The public healthcare rate is indeed 14.6% but half of that is paid by your employer. Of course in the end it doesn’t matter, just that only 7.3% from your gross income will be reduced (also there are rates for nursing care insurance, pension insurance, unemployment insurance – a middle-class income pays 35–50% for tax and insurance).

Public healthcare is obligatory for all employees except you’re earning more than ~65000€/year or are a civil servant. In which case you are entitled for private health care which might be (or in fact is) more expensive but has more options for treatments and some prioritizing on waiting lists and doctor’s appointments.

Family (husband, wife and children) is always insured for free except they are also employed. Children have to pay seperately after reaching age of 25, and if they still study they pay only a low flatrate.

The rate is always 14.6% of gross income except for very low incomes, in which case the employer pays everything, or very high incomes. There is a cap: everything above 65k is not rated – which seems unfair to me.