Add half the bread cubes to the pan. Sprinkle half the sausage and half the cheese on top. Repeat with another layer of bread, sausage and cheese.
In a large bowl, whisk the eggs until beaten. Whisk in the milk, mustard, salt and black pepper until well-blended. Pour the mixture in the pan over the bread. Gently press down on the bread with the back of a fork or a spatula to help the bread absorb the liquid.
Lightly cover the strata, and refrigerate for at least 4 hours or overnight. Remove the strata from the refrigerator about 30 minutes before baking.
Preheat the oven to 325 degrees F.
Bake for 50 to 65 minutes, or until the center appears set and a knife inserted into the center comes out clean. Cool 10 to 15 minutes before cutting and serving.