Preheat oven to 325 degrees F. Grease two large-sized muffin pans with butter and set aside.
Place diced strawberries in a small saucepan over medium-high heat, stirring constantly until berries start to bubble, about 3 minutes. Reduce heat to medium-low and simmer, stirring occasionally, until very thick, about 20 minutes. Remove from heat and set aside to cool completely.
Prepare strawberry cake according to package directions. Pour batter into one of the muffin pans. Bake until a toothpick inserted into the center comes out clean, about 20 minutes. Remove from heat and let cool.
Prepare chocolate cake according to package directions. Pour batter into the remaining muffin pan. Bake until a toothpick inserted into the center comes out clean, about 20 minutes. Remove from heat and let cool.
Meanwhile, place thickened strawberries in the bowl of an electric mixer fitted with a whisk attachment. Add cream cheese and butter, mixing until smooth and creamy. Add powdered sugar ½ cup at a time, beating between additions until all sugar has been added and mixture is thick and smooth. Cover and refrigerate for at least 40 minutes.
While cakes are still in the muffin tins, slice off the domed tops. Remove cakes from muffin tins and slice each cake into two layers.
Place the slightly larger layers (these will be the cake bottoms) on a sheet of wax paper.
Spread strawberry mixture thickly over the bottoms. Cover with remaining layers of cake. Each cake will have both a chocolate and a strawberry layer.
Place 1/3 cup of the chocolate chips in a small bowl and set aside for garnishing.
Place remaining chocolate chips in a microwave safe bowl and heat on high at 30 second intervals, stirring between each interval, until chocolate has melted and is very smooth. Pour over tops of cakes, letting drip down the sides. Let set for 20 minutes at cool room temperature, if serving right away. Or, refrigerate until ready to serve. Cakes can be refrigerated for up to 24 hours.
Garnish tops of cakes with slices of strawberries and reserved chocolate chips before serving.