Travel documents are individual. Ιn order to apply for travel documents you have to be a recognized refugee or an alien with Subsidiary Protection.
If you have International Protection your travel documents and the travel documents of your family are valid for five (5) years. Your travel documents are valid for five (5) years if you are an adult or a minor of fourteen (14) years of age or more. If you are a minor under fourteen (14) years of age your travel documents are valid for three (3) years.
In order to apply for travel documents:
You can apply to the Passport Offices of the Greek Police. You should choose the Passport Office according to your current place of residence. You have to submit an application that is provided by the Passport Office and additional documents/administrative fees that are described HERE. The Passport Office will also take your fingerprints.
When you apply you should have with you your Residence Permit (ADET). If you don't have a Residence Permit your Applicant's Card should have the indication "Residence Permit is Pending." In this case, you need to bring your Applicant's Card with you.
In order to apply for your children's travel documents the same application and supporting documents/administrative fees are required. Further, if your children are above six (6) years old, their fingerprints need to be taken, therefore you should bring your children with you when you submit their application to the Passport Offices.
When you submit your application and supporting documents you will receive a receipt from the Passport Office. You must not lose this receipt as you will need it in order to pick up your travel documents.