Preheat the oven to 350°F. Generously grease a 10" bundt-style or tube pan., In a large mixing bowl, combine the white and brown sugars, the oil, eggs, and vanilla, and beat at medium speed for 1 minute, until smooth., In a medium-sized bowl combine the cocoa, baking soda, baking powder, salt and flour. Add the dry ingredients to the sugar and oil mixture alternately with the warm coffee, beating steadily to make a smooth, thin batter., Spoon the batter into the pan, and sprinkle the chocolate chips on top. Use a spoon or your fingers to barely submerge the chips in the batter; they'll sink and float at random, which is OK., Bake the cake for 60 to 72 minutes, or until a cake tester inserted in the center comes out dry and the top springs back when touched gently., As soon as the cake is out of the oven, gently sprinkle it with the dark and white chocolate. Allow it to rest for several minutes to soften the chips, then swirl the chips onto the cake with a butter knife, spreading and smearing chocolate over the top of the cake.