Melt butter in large skillet over medium heat. Add celery and onion, cook for 10-12 minutes, or until tender.
In a very large bowl, combine crumbled cornbread, stuffing mix, sage, black pepper and cooked celery and onion mixture. Carefully stir.
To mixture, add 2 cups of the chicken broth followed by the lightly beaten eggs. Mix until eggs are incorporated. Slowly add remaining 2 cups of chicken broth, gently stirring. Transfer mixture to large baking dish. Let dressing sit for 10 minutes to allow breadcrumbs to absorb the broth.
Bake in preheated oven at 375°F for 45 to 55 minutes or until top is lightly browned and internal temperature of 165°F is reached.
Notes
Cornbread: The amount from standard 9 x 9 inch pan of cornbread.