We do both also since I'm Jewish and my husband is Catholic. It makes life a bit crazy at times especially when Hanukah and Christmas or Easter and Passover are near each other but since I don't live near any of my family, I know if I don't do the Jewish holidays for my kids (13 and 11), they'll never know their Jewish side (not that the holidays are the only part of being Jewish).
We are visiting my family for Thanksgiving so since Hanukah begins the next night, we will celebrate the first night of Hanukah with my family. Latkes and Kugel here we come!