In a medium-sized bowl, combine the white chocolate pudding mix and 1 3/4 cups of milk. Stir until well blended.
In a separate medium-sized bowl, combine the chocolate pudding mix with the remaining milk. Mix until smooth.
Once both puddings have started to set, use alternating spoonfuls of the two pudding colors and fill a plastic gallon-size baggie.
Close the baggie and snip the end of the tip to pipe the pudding into popsicle molds. The two colors will swirl together beautifully as you pipe.
Freeze the pudding pops for at least 3 hours, or overnight for the best results.
To remove the pudding pops, dip the bottoms of the molds in hot water for a few seconds until they slide out easily.