Copper-diamond composites are increasingly being considered for thermal management applications because of their attractive combination of properties, such as high thermal conductivity (lambda) and low coefficient of thermal expansion (CTE). In this research, thermal properties of Cu-diamond composites with two different types of interfacial carbides (Cr3C2 and SiC) were studied. The interface thermal conductance (h(c)) was calculated with Maxwell mean-field and differential effective medium schemes, wherein experimentally measured lambda was entered as an input parameter. The lambda and h(c) of both the Cu-Cr3C2-diamond and Cu-SiC-diamond composites are higher than those reported in previous studies for Cu-diamond composites with no interfacial carbides. The value of h(c) is intimately related to the morphology and thickness of the interface carbide layer, with the highest h(c) being associated with a thin and continuous interface carbide layer. A lower h(c) resulting from a thicker Cr3C2 layer can provide an alternate explanation for a previously reported trend in lambda of Cu-Cr3C2-diamond composites with different Cr-contents. The experimentally measured CTE was compared with the Turner and Kerner model predictions. The CTE of both the Cu-Cr3C2-diamond and Cu-SiC-diamond composites is lower and better matches the model predictions than the previously reported CTE of Cu-diamond composite with no interfacial carbides. The CTE of Cu-Cr3C2-diamond composites agrees better with the Kerner model than the Turner model, which suggests that deformation during temperature excursions involves shear.