Preheat oven to 250 F. Spread the bread and cornbread cubes out on several cookie sheets and toast until they're dried out. Peek in and stir now and then to prevent too much browning. This takes about an hour.
Meanwhile, saute the vegetables in the butter until translucent and a little bit caramelized.
Transfer the bread and cornbread into a big bowl.
Let everything cool.
Squish the banana up with the herbs until well blended.
Toss banana herb mixture in with the bread.
Pour in the chicken stock just a little at a time, and toss gently.
Use this to stuff the turducken, and/or make more to serve as dressing.
If serving as dressing, bake at 350 F for 45 minutes or so until the top is browned.