On Shabbos Chanukah, we light both the Shabbos candles and the Chanukah candles.
Traditionally, the Shabbos candles are lit by the woman of the house and the Menorah by the man. Kabbalistically, the woman symbolizes the feminine energy of internal focus, and the man represents the external.
By lighting the Shabbos candles, the woman brings peace and spirituality into the home. By lighting the Menorah, the man publicizes spirituality to the outside. These two mitzvahs, these two different energies, are both needed for best effect for the world.
Working together, the feminine and masculine bring powerful energy to their environments, their families and to the relationship.