Prepare cake mix batter according to package directions, adding pudding mix before mixing batter, and folding 1 cup chocolate chips into prepared batter. Transfer to prepared pan. Bake and cool as package directs. Cut into 1/4-inch cubes.
In a large bowl, beat cream cheese and vanilla until blended. Beat in milk until smooth.
In each half-pint jars, layer 1/2 cup cake cubes, 1 tablespoon icing and 1 tablespoon remaining chocolate chips. Repeat layers. Refrigerate leftovers.