Organic–inorganic hybrids have found increasing applications for thermal management across various disciplines. Such materials can achieve thermal conductivities below the so-called “amorphous limit” of their constituents’ thermal conductivity. Despite their technological significance, a complete understanding of the origins of this thermal conductivity reduction remains elusive in these materials. In this paper, we develop a prototypical cross-linked organic–inorganic layered system, to investigate the spectral origins of its sub-amorphous thermal conductivity. Initially, we study the atomic structure of the model and find that besides polymer chain length, the relative drift of the layers governs the reduction in computed basal spacing, in agreement with experimental measurements. We, subsequently, find that organic cross-linking results in up to 40% reduction in thermal conductivity compared to inorganic samples. An in-depth investigation of vibrational modes reveals that this reduction is the result of reduced mode diffusivities, which in turn is a consequence of a vibrational mismatch between the organic and inorganic constituents. We also show that the contribution of propagating modes to the total thermal conductivity is not affected by organic cross-linking. Our approach paves the path toward a physics-informed analysis and design of a wide range of multifunctional hybrid nanomaterials for thermal management applications among others.