You could have the surface dwarfs dig out a rock overhang such that the underdwarfs could drop items to the surface.
I think the ground under the overhang will be [DARK], but I would assume such a setup is still within the spirit of the challenge.
The hole from overdwarf to underdwarf, in a line: Single staircase up, to single channeled tile (open to sky), to single "dug" tile (dug by the underdwarfs as they burrowed in. The "dug" tile is an open hole marked as a garbage dump. Remember, the letter of the challenge is "Every tile the dwarfs can walk on" -- so the hole is a [DARK] location, but the overdwarfs can't walk there because it's a hole (no stairs or ramp). The dump hole being dark means that the landing site under it is also dark, and fair game for the underdwarfs to walk. I use a tileset, so I'm not sure what the actual characters would be, but:
Z +2: Z +1: Z =0:
..## #### ####
...# ./_. _/#_
..## #### ####where # is natural stone, . is open space, _ is a walkable tile, and / is a stairway or ramp. Assume left is "outside" and right is "inside." I *think* you could also do this after the split, by digging an up-ramp where your landing spot will be under the mountain, then removing the ramp before digging the stone out above it from outside. The overdwarf digger would be standing on a [LIGHT] tile, but with the hole already there under it, any stone that gets produced from connecting the two paths would automatically fall into the undertown and still leave the necessary tiles [DARK].
The hole from under to over is a tunneled staircase, to a single tunneled tile which breaks through a sheer wall. A constructed wall and floor (built by the overdwarfs) attach to the sheer wall, leaving a hole through with the underdwarfs can drop goods -- because it's constructed, the tiles it overhangs are [LIGHT] but the underdwarfs can't actually walk on those spaces.
Z +2: Z +1: Z =0:
OO## OO## ####
OO## O._\ __#\
OO## OO## ####where # is natural stone, O is constructed wall or floor, . is open space, _ is walkable ground, and \ is a stairway. Left is still outside, right is still underground.
And yeah, the overdwarfs have a standing military, but all of their arms and armor fall out of the mountain.