Prepare lime jello according to package directions. Pour into a 9×13″ glass baking dish or individual serving dishes (filling each only 1/3 of the way full) and refrigerate until set.
Prepare the lemon jello by adding the powdered gelatin to one cup of boiling water and stirring to dissolve. Add marshmallows and stir until they dissolve as well, whisking if necessary. Whisk in the cream cheese and Miracle Whip, breaking up any clumps of cream cheese, until incorporated. Stir in the drained pineapple, then carefully pour over the set lime layer and return the jello to the refrigerate to set.
Once the middle layer is firm, prepare the cherry jello according to package directions. Carefully pour over the middle layer of jello and return the dish to the refrigerator to set completely. Cut into squares and serve.