Silver opens up interesting perspectives in the fabrication of complex systems based on heteroepitaxial layers after the growth of a silicene layer on its (111) face has been proposed. In this work we explore different synthesis methods of hexagonal boron nitride (h-BN) and graphene sheets on silver. The resulting layers have been examined by high-resolution scanning tunneling microscopy. A comparison of the interfacial electronic band structure upon growth of the distinct two-dimensional (2D) layers has been performed by scanning tunneling spectroscopy and complementary first-principle calculations. We demonstrate that the adsorption of the 2D layers has an effect on the binding energy of the Shockley state and the surface potential by lowering the local work function. These effects are larger in the case of graphene where the surface state of Ag(111) is depopulated due to charge transfer to the graphene. Furthermore, we show that the electronic properties of the h-BN/silver system can be tuned by employing different thicknesses of silver ranging from a few monolayers on Cu(111) to the single crystal Ag substrate.