The thermal conductances across covalently bonded interfaces between oriented single crystal diamond and completely aligned polyethylene chains are determined for the three principal orientations of diamond. The calculated thermal conductances, which range over 690-930 MW m(-2) K(-1), are consistent with those of other strongly bonded interfaces. These results suggest that the experimental interfacial conductances across hard-soft interfaces can be quite large if the bonding across the interface is strong, a conclusion that could have important implications for thermal management in bioelectromechanical systems and other inorganic-organic structures. The effects of defects and cross-linking on the thermal conductivity of polyethylene are also analyzed.