Two-dimensional supramolecular arrays provide a route to the spatial control of the chemical functionality of a surface, but their deposition is in almost all cases limited to a monolayer termination. Here we investigate the sequential deposition of one 2D array on another to form a supramolecular heterostructure and realise growth, normal to the underlying substrate, of distinct ordered layers, each of which is stabilised by in-plane hydrogen bonding. For heterostructures formed by depositing terephthalic acid (TPA) or trimesic acid (TMA) on cyanuric acid/melamine (CA.M) we determine, using atomic force microscopy under ambient conditions, a clear epitaxial arrangement despite the intrinsically distinct symmetries and/or lattice constants of each layer. Structures calculated using classical molecular dynamics are in excellent agreement with the orientation, registry and dimensions of the epitaxial layers. Calculations confirm that van der Waals interactions provide the dominant contribution to the adsorption energy and registry of the layers.