I think you should refer to the information on TheLocal.de which provides a little more clarification on the system.
What paternity pay and/or benefits can I claim?
Mothers are entitled to full pay during the six weeks before, and eight weeks after, the birth, known as "mother protection time".
Both parents can claim parental benefits - if they are on leave during the first 12 months after the child's birth, along with two extra "partner months" of benefit if the couple claims jointly rather than separately.
The benefit is calculated at 65 percent of the parent's previous monthly salary, though it gets boosted slightly if they were earning €1,000 or less. Those with more young children also get a 10-percent (or a minimum of €75 a month) "sibling bonus".
The total benefits are ring-fenced at a minimum of €300 and maximum €1,800 per month, while parents who were unemployed can also claim at least the minimum €300 a month.
Those receiving parental benefit are still allowed to work part-time up to 30 hours a week. And if their existing job is at a company with more than 15 employees, they are entitled to 15 to 30 hours part time work per week, unless the firm has specific reasons for not offering it.
Can I extend my leave?
In general, unplanned extensions and changes to parental leave must be agreed between the parent and their employer. For example, parents can extend their agreed leave with their boss' express approval, but there is no legal entitlement.
And if the employer agrees, a parent can also "carry over" 12 months of their possible three years to be used at any time before the child's eighth birthday.
And for further reading ElternGelt from HowToGermany:
Eligibility for Elterngeld
You should be eligible for Elterngeld if you fulfill the following criteria:
- Have a residence in Germany or an Aufenthaltserlaubnis (residence permit) that allows you to work in Germany
- You and your child reside together
- You care and rear your child personally
- You do not work more than 30 hours per week during the time Elterngeld is issued
And finally subject has been discussed on ExpatBabies which I am not going to quote here to keep readers from having read overload.