Much less, the average monthly cost is about 123 CHF (less than 150$). Source: https://www.bag.admin.ch/de/newnsb/d2okh_kUK_OFhmMDfpyiy

Same in Germany: private kids' insurance costs a fraction of the one for adults. Apparently it's very unlikely that they require expensive healthcare.

Based on what I found, you pay a lower rate for children, but you pay for each child, they don't do a fixed rate for the whole family.