Combine first 10 ingredients in a jar; cover tightly, and shake vigorously. Set marinade mixture aside.
Cut block of Cheddar cheese in half lengthwise. Cut crosswise into ¼-inch-thick slices; set aside. 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. Garnish with fresh parsley sprigs, if desired.
