Parental social insurance or “föräldrarpenning” in Sweden is not as complicated as it might seem. You just have to stay on top of it from month to month.
As you will already be aware Sweden has one of the longest paid family leave quotas in the world. If you are a couple (regardless of whether or not you are married or even if one of you is unemployed) taking care of a new-born you get 480 days to share (roughly 15 to 16 months) EQUALLY (YAY for egalitarianism…).
If you go to the Försäkringskassan website, they have a calculator tool which helps you figure out how much you will receive per month.
Before you get the parental benefit you have to register for it. Register for parental benefit.
Once you have registered, you can apply for the parental benefit which you must keep applying for on monthly basis until your days are used up.