I picked one up for $4 (it's also available in a late night Munchie Meal that tacks on Halfsie fries, two tacos, and a 20-ounce drink for $6).
Upon inspection, the cheese on the grilled cheese portion of my Stacked Grilled Cheese Burger was decidedly not melted (oddly, enough the cheese in the cheeseburger portion was melted...). Not to fret though as they doubled up on the cheese in the top "bun" by including a substantial dollop of warm cheese sauce. The combination of the two ensured warm cheesiness in every bite.
The lettuce, tomato, and pickles were pretty standard as far as fast food goes.
The mayo was actually applied fairly lightly and I didn't catch too much of it.
Overall, Jack in the Box's Stacked Cheese Burger does come off a bit gimmicky (by design I think) and could be much improved by just rearranging the ingredients a little and getting rid of the extra slice of bread.
Nutritional Info - Jack in the Box Stacked Grilled Cheese Burger Munchie Meal (includes fries, tacos, but not including drink)
Calories - 1679 (from Fat - 871)
Fat - 97g (Saturated Fat - 28g)
Sodium - 3538mg
Carbs - 144g (Sugar - 13g)
Protein - 56g