Parents can take unpaid parental leave at the same time. This is called concurrent leave. The second parent can take up to 8 weeks in periods of at least 2 weeks while their partner is also on parental leave. The concurrent leave is deducted from the total unpaid parental leave of 12 months.
One parent may also take flexible unpaid parental leave while the other parent is on unpaid parental leave for a total of 8 weeks.
The Fair Work Ombudsman has information on taking parental leave here.