Thermal and electrical conductivities of 28 layers of 100‐Å‐thick and 6 layers of 500‐Å‐thick polycrystalline copper films, each individually sandwiched between 25‐Å‐thick amorphous Ge or SiO films, have been measured. The results show that, provided no interfacial alloying occurs (as is the case with SiO films), the effective values of the conductivities of the multilayer structure are very close to those of the individual (100 or 500 Å) copper films. This equivalence of the transport behavior enables the measurements of the thermal conductivity of ultrathin metal films. Further, it indicates no significant enhancement of diffuse scattering of electrons and phonons at the surfaces of the copper films due to the presence of multiple interfaces.