Transient thermo-reflectance measurements were made on metals films deposited on Cu film. The Cu film was deposited on Si (001) and sapphire (0001) substrates. The metal films that were deposited include Al, Au, Sn, Zn, and In. The results were modeled using one-dimensional heat equation to determine thermal conductance of interfaces between the metal film and Cu (film/Cu) and Cu and Si (Cu/Si), or Cu and sapphire (Cu/sapphire) in each sample. The results were used to determine the importance of microstructural parameters such as surface roughness, lattice mismatch, solid solubility, and surface energy of the metal film on Cu. The experimental values of interface thermal conductance, although smaller in magnitude, were interpreted in terms of the predicted values by diffuse mismatch model after including the effect of the microstructural parameters. In particular, interface roughness, lattice mismatch, solid solubility, and wettability were found to be important parameters as these are responsible for good atomic level contact between the metal film and Cu.