There are 2 types of government health care system in Japan.
The standard government pension “Kokumin Kenko Hoken” which the contribution is a percentage of your taxable income.
In Yokohama it is a total of 10.48% of your taxable income with a maximum of 890,000 / year.
It is usually sent to your residence with bills to pay each month for 10 months.
There is also another type of health insurance for Employees “Kenkohoken” which is part of social insurance “Shakaihoken” for full time employees.
Usually the company pays half (~15% of salary) and the employee pays the other half.
Health insurance in Japan covers 70% of medical bills and 100% for children under 6.
The 30% can go up to a maximum of 80,000 yen after which the government covers 100% of bills.
The health system in Japan is quite comprehensive and many peopled not find the need to take out extra medical coverage.
For childbirth the government will also pay 420,000 yen which should cover the cost of having a baby at a public hospital.
A private hospital will be from 600,000 ~ and up.