The possibility of 'orbitally selective Mott transitions' within a multi-band Hubbard model, in which one orbital with large on-site electron-electron repulsion U1 is insulating and another orbital, to which it is hybridized, with small U−1, is metallic, is a problem of long-standing debate and investigation. In this paper we study an analogous phenomenon, the co-existence of metallic and insulating bands in a system of orbitals with different electron-phonon coupling. To this end, we examine two variants of the bilayer Holstein model: a uniform bilayer and a 'Holstein-Metal interface' where the electron-phonon coupling (EPC) λ is zero in the 'metal' layer. In the uniform bilayer Holstein model, charge density wave (CDW) order dominates at small interlayer hybridization t3, but decreases and eventually vanishes as t3 grows, providing a charge analog of singlet (spin liquid) physics. In the interface case, we show that CDW order penetrates into the metal layer and forms long-range CDW order at intermediate ratio of inter-to intra-layer hopping strengths 1.4 t3/t 3.4. This is consistent with the occurrence of an 'orbitally selective CDW' regime at weak t3 in which the layer with λ1 = 0 exhibits long range charge order, but the 'metallic layer' with λ−1 = 0, to which it is hybridized, does not.