The influence of the thickness of a thin (1.5-30 nm) copper layer on the thermal boundary conductance (TBC) at the interface between gold and silicon, sapphire and diamond, respectively, was studied using Time Domain Thermoreflectance. Overall, a monotonic increase in the TBC was observed over the first 10 nm, before reaching a plateau. In some cases, it was also observed that an interlayer reduces the TBC as compared to the reference system. This is rationalized by assuming that the TBC evolution as a function of the interlayer thickness is controlled by (i) a contribution of the gold layer that has to be taken into account for all phonons having a wavelength larger than the interlayer thickness and (ii) a thickness-dependent resistance within the interlayer that appears when the electron-phonon coupling is incomplete, i.e., typically over the first 10 nm. A model is proposed in which the contribution to thermal boundary conductance by phonons coming directly from the gold layer is estimated using a simple Debye approximation, while the resistance that appears within the interlayer is estimated by g(T) times h with g(T) the electron-phonon coupling factor and h the interlayer thickness. This results in a system with three resistances in series, i.e., the metal-metal and metal-dielectric interfacial resistances and the interlayer resistance, and a contribution due to phonons of the gold layer. A reasonably good agreement between this model and experimental data is observed. Published by AIP Publishing.