Heat a large skillet over medium-high heat and stir in sausage. Cook and stir until sausage is crumbly, evenly browned, and no longer pink, about 10 minutes. Drain and discard any excess grease.
Lightly grease a 9x13-inch baking dish.
Spread butter on the inside of each English muffin half. Arrange buttered English muffins in the prepared baking dish; top with half the sausage, half the Cheddar cheese, and half the mozzarella cheese.
Whisk eggs, sour cream, and green chilies together in a large bowl; pour evenly over sausage and cheese layer. Top with remaining sausage, Cheddar cheese, and mozzarella cheese. Cover and chill for 8 hours.
Preheat oven to 350 degrees F (175 degrees C).
Bake strata in the preheated oven until lightly browned and set in the middle, about 35 minutes. Let stand for 10 minutes before serving.