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Since its discovery, graphene has been the object of study for several and manifold applications, ranging from photocatalysis to mechanics and electronics of materials. However, the use of pure graphene in certain opto- and microelectronic applications is sometimes limited because of its zero band gap. Among the different methods to widen the band gap, in the present work the attention is focused on the so-called van der Waals composites (or heterostructures, or heterojunctions), namely the stacking of two monolayers of different materials that are held together by weak van der Waals interactions. An interesting composite is the graphene/molybdenite (MoS2) heterostructure, where the second material is a bidimensional semiconductor characterized by strong in-plane covalent bonds and weak out-of-plane interactions, which means that it is possible to exfoliate MoS2 into monolayers of atomic thickness. Also, from the crystallographic point of view, both graphene and the monolayer of molybdenite (MoS2-1H) have a 2D hexagonal lattice and their stacking could be structurally favourable. In this work, the electronic band structure and density of states, complex dielectric function and optical properties of the stacked van der Waals bilayer heterojunction graphene/MoS2-1H were calculated and compared to both the single monolayers of graphene and molybdenite, to understand how the interaction between the two materials may alter the above cited properties. The analysis of the band structure in this van der Waals composite clearly showed a small direct band gap related to the transition π → π ∗ (ca. 2.5 meV) in correspondence of the high symmetry point K. The heterojunction showed also, as expected, some important variations in the complex dielectric function and related properties in the visible-light spectral region. The results obtained in the present work could be of use for future development and applications of this kind and similar 2D composite materials with tailored electronic and optical properties.