My girlfriend not working in German: Health insurance?

Hello,

My girlfriend and me live in Germany - a few months ago she gave birth
to a baby so she does not work anymore - We have been living in Germany
for 4 years, I do work for a German company, she was working remotly in
Germany for an English company, so she never has the status of German
worker whatsoever.
Now comes the end of her maternity leave and we do not know what can be
done as far as her health insurance is concerned:
She was on private Versi. before her maternity (her company was paying
for it)
Her maternity leave is over
She does not go back to work (at least not for the next year)
We are not married, so I cannot put her on my insurence (our son is,
though)
We are not planning on getting married because "we have to" because of
the health insurence ...
Does anybody have a tip? Could she join the public versi. in some way?
Private is way too expensive :-/

Thanks!

.