Cut the cornbread and French bread into 1-inch cubes, place on a baking sheet and leave out until completely dried out, several hours or overnight.
Preheat the oven to 375 degrees F.
Add the bacon to a skillet and saute over medium heat until cooked and almost crisp, about 7 minutes. Remove to a plate and wipe out any grease. Melt the butter in the skillet, throw in the celery, red peppers and onions and cook, stirring, until very soft, 4 to 5 minutes. Add the jalapenos and garlic and continue to saute for 2 minutes. Pour in the chicken broth, add the parsley, rosemary and some salt and pepper and stir. Cook for a couple of minutes, then turn off the heat.
Add the bread and bacon to a large bowl and spoon in some of the broth mixture. Keep adding the broth, tossing as you go, until it is all mixed in. Add more salt and pepper if needed and toss it around, then check the seasoning. If you like your dressing extra moist, add a little more broth.
Pile the dressing into a 3-quart (9-by-13-inch) casserole pan and bake, uncovered, until golden, 25 to 30 minutes. Serve piping hot.
Preheat the oven to 450 degrees F.
Add the cornmeal to a large bowl along with the flour, baking powder, salt, basil, sage and thyme and stir together.
Measure the buttermilk in a measuring cup, add the whole milk and egg and stir together with a fork. Add the baking soda and stir. Pour the milk mixture into the dry ingredients and stir with a fork until just combined. Do not overmix.
In a small microwave-safe bowl, melt 2 tablespoons butter and 2 tablespoons shortening in the microwave and slowly add to the batter, stirring constantly until combined.
In a 10-inch cast-iron skillet over high heat, melt the remaining tablespoon of butter and shortening. Pour the batter into the hot skillet, spread to even out the surface and cook over high heat for 1 minute. Then get it into the oven straightaway and bake until golden brown, 20 to 25 minutes. The edges should be crispy.
If you are making the dressing ahead, hold back some broth to add on serving day.