Private health insurance
The monthly cost remains the same. You're responsible for the full amount from the start of the maternity leave until the end of the maternity or parental leave - even if you are employed.
Public health insurance
If you are mandatory insured (employed and you earn less than the private insurance threshold), the insurance is free until you come back to work, both during the maternity and parental leave. You do not pay contribution on Elterngeld (benefit paid by the state) neither Mutterschaftgeld (benefit paid by the statutory health insurance provider) and Arbeitgeber-Zuschuss (benefit paid by the employer). You will only have to pay additional contribution if you are doing a part-time job. (minijobs - up to €538/month do not count towards it, and are still free of contribution).
If you are voluntary insured (self-employed or employed and earn more than the private insurance threshold), the insurance is also going to be free until you start working again. You do not pay contribution on Elterngeld and Mutterschaftgeld.
However, additionally, contribution will have to be paid for the following income:
Renting and leasing,
Capital assets, shares and similar
Maintenance that must be paid due to legal obligations, for example from divorced spouses
If your spouse is privately insured, his or her income will be taken into account when calculating your contributions.
In order to even that out, voluntary insured people will receive a bit higher Elterngeld.
Monthly earnings of voluntary insured people under €538 might also be free of contribution. Best to check that with your health insurance provider directly.
Self-employed people do not need or have the right to the actual Elternzeit/parental leave in the real sense of the word, since they do not even have employer. But they do, as mentioned, have the right to the Elterngeld for the time they are not working.
It is also worth to note that Self-employed mothers only receive Mutterschaftsgeld if they contracted sick-day payments with the public provider. And since there is no employer to provide the bigger part of the income during the maternity leave (Arbeitgeber-Zuschuss), we advise contracting the sick-day payment from your public insurance provider.