Reduction of cross-plane thermal conductivity and understanding the mechanisms of heat transport in nanostructured metal/semiconductor superlattices are crucial for their potential applications in thermoelectric and thermionic energy conversion devices, thermal management systems, and thermal barrier coatings. We have developed epitaxial (Ti,W)N/(Al,Sc)N metal/semiconductor superlattices with periodicity ranging from 1 nm to 240 nm that show significantly lower thermal conductivity compared to the parent TiN/(Al,Sc)N superlattice system. The (Ti,W)N/(Al,Sc)N superlattices grow with [001] orientation on the MgO(001) substrates with well defined coherent layers and are nominally single crystalline with low densities of extended defects. Cross-plane thermal conductivity (measured by time-domain thermoreflectance (TDTR)) decreases with an increase in the superlattice interface density in a manner that is consistent with incoherent phonon boundary scattering. Thermal conductivity values saturate at 1.7 W/m-K for short superlattice periods possibly due to a delicate balance between long wavelength coherent phonon modes and incoherent phonon scattering from heavy tungsten (W) atomic sites and superlattice interfaces. First-principles density functional theory based calculations are performed to model the vibrational spectrum of the individual component materials and transport models are used to explain the interface thermal conductance (ITC) across the (Ti,W)N/(Al,Sc)N interfaces as a function of periodicity. The long-wavelength coherent phonon modes are expected to play a dominant role in the thermal transport properties of the short-period superlattices. Our analysis of the thermal transport properties of (Ti,W)N/(Al,Sc)N metal/semiconductor superlattices addresses fundamental questions about heat transport in multi-layer materials.