Set out two 1 1/2-by-3 1/2-by-60-inch boards on top of each other, so they line up perfectly. Screw them together, with 2 3/4-inch wood screws, spaced every 12 inches apart; don't pre-drill due to the chance of splitting. Repeat for three other pairs of 1 1/2-by-3 1/2-by-60-inch boards to create the four posts of the bunk bed.
Set out two of the bunk bed posts parallel to each other about 3 feet apart. Position a 1 1/2-by-3 1/2-by-36-inch board across the two posts so that the ends of this board, which is a side support board, become even with the outside edges of the posts. Arrange the side support board so that its center is 1 foot from one end of the posts.
Attach the side support board to the posts using 2 3/4-inch wood screws, four to each joint. Repeat to add another side support board that is 4 feet from the same end of the post so that there are two side support boards spanning the posts. Repeat with another set of two posts and two side support boards to form the head and foot of the bunk bed.
Have two assistants hold upright the head and foot of the beds so that the end of the posts that were measured from are upright and the side support boards are facing inward. Position a 1 1/2-by-3 1/2-by-83-inch board between the head and foot of the bunk bed, level with the bottom side support board on both the head and the foot. Adjust the spacing of the head and the foot until the ends of this new long board are even with the outside edges of the head and foot.
Drill four holes through the long board and into the head and foot. Fasten the boards together with 2 3/4-inch wood screws in these holes. Repeat with two more holes and screws through the long board and into each side support board. Follow the same procedure to add long boards to each of the other three support board positions.
Spread out six 1 1/2-by-3 1/2-by-39-inch boards on each pair of long boards, evenly spaced. Drill two holes through each of these mattress support boards and into each of the long boards, for a total of 48 holes. Secure them in place with 2 3/4-inch screws.
Sand the entire surface of the bunk bed to eliminate any splinters and resulting air mattress leaks. Set the air mattresses in place on top of the mattress support boards.