Slit chiles lengthwise on one side.
Remove seeds and drain.
Slice Monterey Jack cheese into 1/4-inch thick slices and place inside chiles.
Place stuffed chiles in an ungreased 3 quart baking dish.
Mix eggs, milk, flour, salt and pepper well and pour over chiles.
Sprinkle top with grated Cheddar cheese.
Bake uncovered at 350 F for 45 minutes.