1. Whisk together first 6 ingredients. Set aside.
2. Cut Monterey Jack cheese in half lengthwise. Cut each half crosswise into 1/4-inch-thick slices. Repeat with Cheddar cheese and cream cheese.
3. Arrange cheese in 4 rows in a shallow 2-qt. baking dish, alternating Monterey Jack cheese, Cheddar cheese, and cream cheese. Pour marinade over cheese. Cover and chill at least 8 hours.
4. Drain marinade; arrange cheese on a platter in rows. Top with pimiento, and serve with assorted crackers.