Phase separation of multivalent protein and RNA molecules underlies the biogenesis of biomolecular condensates such as membraneless organelles. In vivo, these condensates encompass hundreds of distinct types of molecules that typically organize into multilayered structures supporting the differential partitioning of molecules into distinct regions with distinct material properties. The interplay between driven (active) versus spontaneous (passive) processes that are required for enabling the formation of condensates with coexisting layers of distinct material properties remains unclear. Here, we deploy systematic experiments and simulations based on coarse-grained models to show that the collective interactions among the simplest, biologically relevant proteins and archetypal RNA molecules are sufficient for driving the spontaneous emergence of multilayered condensates with distinct material properties. These studies yield a set of rules regarding homotypic and heterotypic interactions that are likely to be relevant for understanding the interplay between active and passive processes that control the formation of functional biomolecular condensates.