We model the two-dimensional self-assembly of planar molecules capable of complementary interactions (like hydrogen bonding) as a set of hexagonal tiles on a hexagonal lattice. We use Monte Carlo simulations to study the phase diagrams of three model systems. The phases are characterized using a variety of order parameters, and they are studied as a function of the strength of the complementary interaction energy. This simplified model is proven to be capable of reproducing the phases encountered in real systems, unifying within the same framework most of the structures encountered experimentally.