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The thermal conductivity of crystalline materials cannot be arbitrarily low, as the intrinsic limit depends on the phonon dispersion. We used complementary strategies to suppress the contribution of the longitudinal and transverse phonons to heat transport in layered materials that contain different types of intrinsic chemical interfaces. BiOCl and Bi₂O₂Se encapsulate these design principles for longitudinal and transverse modes, respectively, and the bulk superlattice material Bi₄O₄SeCl₂ combines these effects by ordering both interface types within its unit cell to reach an extremely low thermal conductivity of 0.1 watts per kelvin per meter at room temperature along its stacking direction. This value comes within a factor of four of the thermal conductivity of air. We demonstrated that chemical control of the spatial arrangement of distinct interfaces can synergically modify vibrational modes to minimize thermal conductivity.