Graphite-like hexagonal AlN (h-AlN) multilayers have been experimentally manifested and theoretically modeled. The development of any functional electronics applications of h-AlN would most certainly require its integration with other layered materials, particularly graphene. Here, by employing vdW-corrected density functional theory calculations, we investigate structure, interaction energy, and electronic properties of van der Waals stacking sequences of few-layer h-AlN with graphene. We find that the presence of a template such as graphene induces enough interlayer charge separation in h-AlN, favoring a graphite-like stacking formation. We also find that the interface dipole, calculated per unit cell of the stacks, tends to increase with the number of stacked layers of h-AlN and graphene.