Thin films of disk-shaped molecules are expected to display anisotropic optical and transport properties, leading to applications in optical display or sensor technologies. Bilayer Langmuir-Blodgett films of monomeric triphenylene mesogens have been studied by atomic force microscopy. The triphenylene cores of the constituent molecules tend to promote the formation of columnar structures in the plane of the substrate and along the direction of deposition of the film. Atomic force microscopy images of bilayer Langmuir-Blodgett films revealed two types of structure, one corresponding to an aligned columnar structure and the other to an unusual square lattice, which may result from the superposition of columnar structures in adjacent layers that intersect at near right angles. Annealing such bilayers near the melting point of the bulk compound improved the structural ordering by reducing the angular spread of orientations associated with the well-developed columnar structure in some areas and by producing a more distinct square lattice in other areas of the sample.