Place bread cubes in a greased 13x9-in. baking dish. In a large skillet, cook sausage with pepper and onion over medium-high heat until no longer pink, 5-7 minutes. With a slotted spoon, place sausage mixture over bread. Sprinkle with cheese.
In a large bowl, whisk together eggs, mustard and milk; pour over top. Refrigerate, covered, overnight.
Preheat oven to 350°. Remove strata from refrigerator while oven heats. Bake, uncovered, until a knife inserted in centre comes out clean, 30-35 minutes. Let stand 5 minutes before cutting