How can my husband get a residency card in Greece and what insurance does he need?

Your husband has 3 months, starting from the day of legal entry, to apply for a residence permit as the “family member of a Greek citizen”. The insurance is a private one. A temporary residence permit is initially granted. The permanent residence permit, under which the citizen of a third country needs to travel to other Schengen countries, takes much time to be issued; it requires residence in Greece at least 6 months per year and is granted for 5 years. After five years, it is renewable for 10 years if it is proved that he resides in Greece for at least 6 months per year. Also, this permit provides access to any form of work.

He could apply for a 5-year residence as the spouse of a Greek citizen. He must get a private health insurance.