Heat oven to 375°F. Using 1 tablespoon of the butter, generously grease 12-cup fluted tube pan. In small microwavable bowl, microwave remaining butter uncovered on High about 1 minute or until melted when stirred.
Separate cans of dough into 16 rolls; cut each in half crosswise. Place half of roll pieces in pan. Sprinkle with half of the pudding mix and half of the brown sugar. Drizzle with half of the melted butter. Repeat layering with remaining roll pieces, pudding mix, brown sugar and melted butter. Sprinkle with chocolate chips.
Bake 24 to 28 minutes or until rolls are deep golden brown and dough appears done when slightly pulled apart. Cool in pan 2 minutes. Turn upside down onto serving platter. Cool 15 minutes.
Remove lids from icings. Microwave icings on High 10 to 15 seconds or until thin enough to drizzle. Drizzle over warm coffee cake. Cut into wedges. Serve warm.