Strong in-plane bonding and weak van der Waals interplanar interactions characterize a large number of layered materials, as epitomized by graphite. The advent of graphene (G), individual layers from graphite, and atomic layers isolated from a few other van der Waals bonded layered compounds has enabled the ability to pick, place, and stack atomic layers of arbitrary compositions and build unique layered materials, which would be otherwise impossible to synthesize via other known techniques. Here we demonstrate this concept for solids consisting of randomly stacked layers of graphene and hexagonal boron nitride (h-BN). Dispersions of exfoliated h-BN layers and graphene have been prepared by liquid phase exfoliation methods and mixed, in various concentrations, to create artificially stacked h-BN/G solids. These van der Waals stacked hybrid solid materials show interesting electrical, mechanical, and optical properties distinctly different from their starting parent layers. From extensive first principle calculations we identify (i) a novel approach to control the dipole at the h-BN/G interface by properly sandwiching or sliding layers of h-BN and graphene, and (ii) a way to inject carriers in graphene upon UV excitations of the Frenkell-like excitons of the h-BN layer(s). Our combined approach could be used to create artificial materials, made predominantly from inter planar van der Waals stacking of robust bond saturated atomic layers of different solids with vastly different properties.