This paper describes dynamic self-assembly of millimeter-sized, magnetized disks floating at two parallel interfaces and spinning under the influence of a rotating, external magnetic field. All disks experience a central, confining magnetic potential, and interact with one another hydrodynamically both in the plane of the interface, and between the interfaces. The interactions between the disks spinning on different interfaces are repulsive for low rotational speeds, and attractive for high rotational speeds. The interplay between magnetic and hydrodynamic forces acting in the system leads to the formation of quasi three-dimensional, ordered aggreates. Changing the rotation speeds of the disks can reversibly change the morphologies of these aggregates.