Preheat oven to 350. Grease and flour two 9 inch round baking pans.
Combine water and coffee granules in medium bowl. Stir in creamer with wire whisk. Combine 1 2/3 cups flour and baking soda in another medium bowl. Microwave chips and oil in large, uncovered, microwave-safe bowl on medium-high (70%) for 1 minute; stir. Morsels may retain some of their shape. If necessary, microwave at additional 10 to 15 second intervals, stirring just until melted. Add coffee mixture, sugar, eggs, evaporated milk, vinegar and vanilla extract to melted chips; mix with wire whisk. Gradually beat in flour mixture until combined. (Batter will be thin.) Pour 3 1/4 cups batter into medium bowl; stir in remaining flour. Pour into prepared pans.
Blend cocoa into remaining batter with wire whisk until blended. Slowly pour even amounts of cocoa batter into the center of each pan.
Bake for 40 to 45 minutes or until wooden pick inserted in centers comes out clean. Cool in pans on wire racks for 10 minutes; invert onto wire racks to cool completely.
Micorwave chips and butter in large, uncovered, micorwave-safe bowl on medium-high (70%) for 1 minute; stir. Chips may retain some of their shape. If necessary, microwave at additional 10-15 second intervals, stirring just until melted. Combine coffee granules and water in small bowl. Beat cream cheese and coffee mixture into melted chips. Gradually beat in powdered sugar until mixture reaches spreading consistency.
Spread frosting between layers and over top and sides of cake.