Preheat the oven to 350 degrees. Using a large bowl, combine the softened cream cheese, mayonnaise, garlic, and 1/4 cup of each the Monterrey jack and Parmesan cheese (reserving 1/4 cup for topping). Mix thoroughly until combined.
Heat the frozen spinach in the microwave according to package instructions. Let it cool, and then drain it very well and squeeze any access water out of the spinach.
Roughly chop the artichoke hearts and jalapenos. Add all of the veggies to the cheese mixture and stir well to combine. Squeeze the lemon juice, and add the salt and pepper and mix well.
Pour the dip into a baking dish that has been sprayed with non-stick cooking spray. Bake for 15 minutes.
Remove the dip from the oven and sprinkle the remaining Parmesan and Monterrey jack cheese over the top. Place back in the oven and bake for an additional 10 minutes.