Preheat the oven to 325 degrees F and spread the rye and cornbread cubes out on 2 rimmed baking sheets. Bake until golden and toasted, 20 to 25 minutes. Let cool. Lower the oven to 375 degrees F.
Cook the sausage meat in a skillet over medium-high heat, breaking up with a spoon, until browned, 5 minutes. Set aside.
Grease a 9- by 13-inch baking dish with butter or gluten-free cooking spray. In a large skillet, melt the butter over medium heat. Add the onion, celery and mushrooms; season with salt and pepper, and cook until softened and the liquid has evaporated, about 10 minutes. Transfer to a large bowl. Add the toasted rye cubes, toasted cornbread cubes, cooked sausage and about 3/4 teaspoon salt and 1/4 teaspoon pepper.
In a medium bowl, whisk together the broth, cream, eggs, raisins, parsley and caraway seeds; pour over the bread mixture and toss to evenly coat. Transfer to the prepared baking dish and bake, uncovered, until golden, about 30 minutes. Serve immediately.
Recipe courtesy of Silvana Nardone, silvanaskitchen.com