We report the synthesis of heterostructures composed of graphene and boron nitride (BN) films. The BN was synthesized by short-pulse laser-plasma deposition while graphene was synthesized by hot filament chemical vapor deposition. The heterostructures were fabricated by two different sequences: graphene deposited on BN and BN deposited on graphene. The crystalline quality of the BN-graphene and graphene-BN heterostructures was evaluated by Raman spectroscopy mapping and temperature-dependent Raman spectroscopy to analyze the phonon-phonon interactions in these layered structures. The physical properties of the heterostructured films were carefully studied by: optical transmittance, sheet resistance, thermal conductivity, band-gap, X-ray diffraction, scanning electron microscopy, X-ray photoelectron spectroscopy, transmission electron microscopy and electron energy loss spectroscopy. The advantages and disadvantages of each sequential deposition process are discussed in terms of the crystalline quality and physical properties of the BN-graphene and graphene-BN heterostructures.