Whisk together first 3 ingredients until mixture is blended; stir in diced red peppers and next 6 ingredients. Set marinade aside.
Cut block of Cheddar cheese in half lengthwise. Cut halves crosswise into 1/4-inch-thick slices. Repeat procedure with Monterey Jack cheese and cream cheese.
Arrange cheese slices alternately in a shallow baking dish, standing slices on edge. Pour marinade over cheeses. Cover and chill at least 8 hours. Transfer cheese to a serving plate, and spoon remaining marinade over top. Serve with assorted crackers.