Preheat the oven to 350 degrees F. Butter a 14-inch dutch oven or 9 x 13-inch casserole dish.
In a medium saucepan, add the turkey and chicken. Cover with water and bring to a boil over medium-high heat for about 15 minutes or until fork tender. Set aside to cool then shred the chicken and chop the turkey.
In a large cast iron skillet, melt the butter over medium heat then stir in the onion and celery. Cook for about 5 minutes or until tender, stirring occasionally.
In a large mixing bowl, mix together the onion, celery, stuffing mix, crumbled cornbread, chicken broth, sage and poultry seasoning. Stir in the turkey and chicken. Let it set a couple minutes to absorb the liquid. If there is excess liquid pooling along the edges add up to 1/2 cup more crumbled cornbread.
Spoon the dressing mixture in the Dutch oven or casserole dish. Cover and place in the icebox overnight or until ready to cook. Take the dish out of the icebox about 30 minutes before baking.
Evenly spread the cream of chicken soup over the top. Bake for 45 to 50 minutes or until the top is golden brown and the mixture sets up and is sponge-like. Let rest 10 minutes before serving.