Yes, you will be reimbursed for expenses you pay to the maternity hospital. The percentage depends on the municipal government, so I can't say how much.
When I had my babies 20-some years ago, I had all of the hospital expenses covered and a little more, and that was at a municipality in Kanagawa Prefecture for the first baby and a municipality of Tokyo for the second. So, the percentages were different. And that was with kokumin kenko hoken, since my husband and I didn't have corporate employers and therefore no "kouseinenkin hoken."
I don't know how much you can get, but considering the government concern regarding the falling birth rate, I guess you can get covered substantially and might even get a bonus. You should consult the local municipal government on how much you are entitled to receive.