The short answer is yes, if you pay for the cover to extend to your family.
When you join a company that offers private health insurance (like MBB), you will have a choice to also sign up your significant others. If you live in a country where Private Health Insurance is a taxable benefit (e.g. the UK), then you will also have to pay tax on their policy. Once you do this, your partner will get the same exact benefits as you. So if the policy covers childbirth for the employee (which most policies will), then it will also cover it for your spouse.