We report on the microstructure, morphology, and growth of 5,5'-bis(naphth-2-yl)-2,2'-bithiophene (NaT2) thin films deposited on graphene, characterized by grazing incidence X-ray diffraction (GIXRD) and complemented by atomic force microscopy (AFM) measurements. NaT2 is deposited on two types of graphene surfaces: custom-made samples where chemical vapor deposition (CVD)-grown graphene layers are transferred onto a Si/SiO2 substrate by us and common commercially transferred CVD graphene on Si/SiO2. Pristine Si/SiO2 substrates are used as a reference. The NaT2 crystal structure and orientation depend strongly on the underlying surface, with the molecules predominantly lying down on the graphene surface (face-on orientation) and standing nearly out-of-plane (edge-on orientation) on the Si/SiO2 reference surface. Post growth GIXRD and AFM measurements reveal that the crystalline structure and grain morphology differ depending on whether there is polymer residue left on the graphene surface. In situ GIXRD measurements show that the thickness dependence of the intensity of the (111) reflection from the crystalline edge-on phase does not intersect zero at the beginning of the deposition process, suggesting that an initial wetting layer, corresponding to 1-2 molecular layers, is formed at the surface-film interface. By contrast, the (111) reflection intensity from the crystalline face-on phase grows at a constant rate as a function of film thickness during the entire deposition.