Combine first 10 ingredients, stirring with a whisk.
Cut block of Cheddar cheese in half lengthwise. Cut crosswise into 1/4-inch-thick slices. Repeat procedure with cream cheese. Arrange cheese slices alternately in a shallow baking dish, standing slices on edge. Pour marinade over cheese slices. Cover and marinate in refrigerator at least 8 hours.
Transfer cheese slices to a serving platter in the same alternating fashion, reserving marinade. Spoon marinade over cheese slices. Serve with whole wheat crackers (crackers not included in analysis).