Prepare cornbread mix and biscuits according to package directions; let cool. Crumble cornbread and biscuits in a large bowl. Set aside.
Melt butter in a large skillet over medium-high heat; add onion and celery, and sauté until tender. Add sautéed vegetables, broth, and remaining ingredients to crumbled cornbread; stir well. Spoon dressing into a lightly greased 13" x 9" baking dish.
Bake, uncovered, at 350° for 55 minutes or until browned.
Make-Ahead Note: Prepare recipe as directed; do not bake. Cover and freeze dressing up to 3 months or refrigerate up to 24 hours. Remove from refrigerator; let stand 30 minutes. Uncover and bake as directed.