All babies and minors are required to have their own passport when travelling to any country which is not part of the European Union Schengen area (note: not all EU countries are signatories to the Schengen agreement). Please note that if you are travelling within the Schengen area (see this website for a list of countries in the Schengen area), you are still advised to take your and your baby’s passport or ID card with you, so you can prove your identity, if required (e.g. if stopped by police).
Even if only one of the parents is Dutch, the child is still eligible to obtain a Dutch passport. However, if neither of you are Dutch citizens, your child is not entitled to a Dutch passport, irrespective of where the child was born. Under these circumstances, you should apply for a passport for your child from either your embassy or the national passport office in your native country.