Place chicken in a small pot with enough water to cover. Bring to boil, reduce heat, and simmer for 30 minutes or until chicken is done.
Remove chicken from pot, set aside to cool. Remove skin and bones; chop meat and save for dressing. Strain, and reserve broth.
Preheat oven to 375 degrees F (190 degrees C). Lightly grease two 4-quart casserole dishes.
In a large bowl, combine cornbread, biscuits, chicken soup, onion, celery, salt, pepper, sage and eggs. Stir well. 30 minutes before baking, add a desired amount of reserved chicken and enough broth to soak dressing. Divide dressing between prepared baking dishes.
Bake in preheated oven until top is browned and center is firm, about 30 minutes.