Defect-induced magnetism in dilute magnetic semiconductors challenges our understanding of magnetism in solids. Theories based on conventional superexchange or double-exchange interactions cannot explain long range magnetic order at concentrations below the percolation threshold in these materials. On the other hand, the codoping-induced magnetism, which can explain magnetic interactions below the percolation threshold, has eluded explanation. In this work we propose that defect-induced magnetism in codoped non-magnetic materials can be viewed within a molecular generalization of the atomic double-exchange and superexchange interactions applied to an arbitrary bipartite lattice hosted by (or embedded in) defect-free non-magnetic materials. In this view, the crucial factor for the development of magnetism appears to be the defect complementarity of the codopants. We demonstrate this by taking ZnO and GaN (the most widely studied doped oxide and nitride magnetic semiconductors, respectively) as host materials and perform theoretical calculations using ab initio methods after codoping them with transition metal impurities for a variety of configurations. Our results indicate that the magnetic coupling among the induced and/or doped magnetic moments takes the form of an interaction among spin-polarized molecular units which is facilitated by the formation of the hosted bipartite codopant structures. The universality of the proposed mechanism is further supported by earlier results referring to the rhombohedral C(60)-based polymers.