Combine all marinade ingredients in a jar; cover tightly and shake vigorously. Set aside.
Make sure cheeses are well-chilled (you can put them in the freezer for about 20 minutes).
Cut block of cheddar in half lengthwise; then cut crosswise into 1/4"-thick slices. Set aside. Cut the cream cheese, following the same procedure.
Arrange cheese slices alternately in a shallow baking dish, standing slices on edges.
Pour marinade over cheese slices. Cover and refrigerate at least eight hours.
To serve, transfer cheese slices to a serving platter in the same alternating pattern. Spoon marinade over the cheese. Serve with assorted crackers