We study the thermal conductance across solid-solid interfaces as the composition of an intermediate matching layer is varied. In the absence of phonon-phonon interactions, an added layer can make the interfacial conductance increase or decrease depending on the interplay between (1) an increase in phonon transmission due to better bridging between the contacts and (2) a decrease in the number of available conduction channels that must conserve their momenta transverse to the interface. When phonon-phonon interactions are included, the added layer is seen to aid conductance when the decrease in resistances at the contact-layer boundaries compensate for the additional layer resistance. For the particular systems explored in this work, the maximum conductance happens when the layer mass is close to the geometric mean of the contact masses. The surprising result, usually associated with coherent antireflection coatings, follows from a monotonic increase in the boundary resistance with the interface mass ratio. This geometric mean condition readily extends to a compositionally graded interfacial layer with an exponentially varying mass that generates the thermal equivalent of a broadband impedance matching network.