Bilhah and Zilpah were “handmaidens” to Rachel and Leah and were “given” to Jacob in order to bear children for their mistresses. Bilhah gave birth to Dan and Naphtali, and Zilpah gave birth to Gad and Asher. Even though these women were mothers of 1/3 of the 12 Tribes of Israel, they are not counted as foremothers, and are not included in the imahot blessings.
While there are all sorts of logically-twisted reason for this (such as how Bilhah and Zilpah also had lofty souls, but not as lofty as the Matriarchs), the real reason is of course social status in ancient communities and how those statuses live on. Rachel and Leah were the property of first their father and then their husband, and their “handmaidens” were property of property.
As a feminist havurah – one that pays attention to how power is expressed through gender – we actively choose to create a prayer life that doesn’t go on re-enacting “women as property.” So we list the names of our Jewish ancestors during the amidah, we include Bilhah and Zilpah. To us, they represent all of the Jews who have not been fully counted as equals in the U.S. Jewish world: converts, BIJOCSM, poor Jews, Jews of patrilineal but not matrilineal descent, organizers and outsiders of every variety.