Cook the onion in the butter till soft. Add ½ teaspoon salt, ¼ teaspoon pepper, and nutmeg and cook, stirring, for about a minute. Mix in spinach, then remove from heat.
Spread about a third of the bread cubes in a buttered 9 x 13 dish and top evenly with a third of the spinach mixture. Sprinkle with a third of each cheese. Repeat with two more layers of each component.
Whisk together milk, eggs, mustard, and remaining ½ teaspoon salt and ¼ teaspoon pepper and pour over strata. Cover with plastic wrap and refrigerate for at least 8 hours.
Preheat oven to 350°. Let strata sit at room temperature for about a half hour before baking.
Bake uncovered till golden and cooked through, 45 to 55 minutes. Let stand 5 minutes before serving.
