Preheat oven to 350 degrees. Lightly oil three 9-inch cake pans and line the bottoms with a circle of parchment paper.
Into a large bowl sift the flour, cocoa, baking soda, baking powder, and salt. Add the sugar and whisk to combine. In a medium bowl whisk together the water, milk, vanilla, oil, vinegar, and coffee.
Pour the wet mixture into the dry and whisk just until mixed, with no visible dry flour remaining. Divide the batter evenly among the three pans, and bake 28 to 32 minutes or until the tops bounce back when lightly pressed.
Allow the cakes to cool in the pans for about 10 minutes then transfer to racks to cool completely. If preparing in advance, wrap each layer individually in plastic wrap, and store in the refrigerator.
Make the frosting:
With a blender or spice grinder, process the freeze-dried raspberries until powdered. Place a mesh strainer over a bowl, and pour the powdered raspberries through the strainer to separate the seeds. Discard the seeds, and set the raspberry powder aside.
Using a handheld or stand mixer, cream together the room temperature cream cheese and butter until light and fluffy, about 5 minutes. Add sifted powdered sugar 1 cup at a time, beating on low speed between additions and scraping down the sides of the bowl as needed. Taste for sweetness, adjusting as desired. Add raspberry powder 1 tablespoon at a time until the desired color and flavor are reached (I used 3 Tbsp powder for a light pink frosting; you should have some powder leftover). Beat on medium/high speed until fully incorporated and smooth. If the frosting seems too soft for decorating the cake, place the bowl in the refrigerator for 15 to 20 minutes. If making in advance, store the frosting in an airtight container in the refrigerator.
Assemble the cake:
Place one cake layer on a serving plate or cake stand. Spread about ¼ to ⅓ cup raspberry jam on top of the cake (refer to photos above). Using an offset spatula spread a thin layer of frosting on top of the jam. Repeat the process for the second layer.
Place the 3rd cake layer and frost the top and sides. Decorate with fresh berries. Sift raspberry powder and powdered sugar on top if desired.
Notes
Refrigerate the decorated cake until ready to serve. Store leftovers in an airtight container in the refrigerator for up to 4 days. Due to the cream cheese in the frosting I don't recommend freezing this cake. However, unfrosted cake layers can be frozen for up to one month. Allow to thaw in the refrigerator overnight.