In a medium bowl, combine pudding mix and milk with a whisk until smooth. Slowly stir in whipped topping.
Divide in half and color one half red using food coloring as desired (I recommend gel food coloring as it is more concentrated and is less likely to turn pink).
Spoon 1-2 tbsp of red pudding mixture into the bottom of 6-7 popsicle molds. Freezer for 1 hour or until firm.
With your finger, wet one side of a small, sliced strawberry with a bit of water. Lay it, wet side down, onto the side of the popsicle mold where you want it to freeze and stay in place (see the image below). Freeze for 1-2 hours or until the strawberry is frozen in place.
Top with white pudding mixture, enough to cover your strawberry. Freeze 1 hour, then top with 1-2 tbsp red pudding mixture and freeze 2-3 hours until firm.
To unmold, run under luke warm tap water for 1-2 minutes.