We have fabricated a model system of precisely layer-engineered inorganic-organic thin-film structures using atomic/molecular-layer deposition (ALD/MLD). The samples consist of nanoscale polycrystalline ZnO layers and intervening benzene layers, covering a broad range of layer sequences. The samples characterized in this study combined with previous publications provide an excellent sample set to examine thermal transport properties in inorganic-organic thin films. The cross-plane thermal conductivity is found to depend on multiple factors, with the inorganic-organic interface density being the dominating factor. Our work highlights the remarkable capability of interface engineering in suppressing the thermal conductivity of hybrid inorganic-organic materials, e.g., for thermoelectric applications.