The possibility of a ferrimagnetic spin alignment in a novel type of alternating heterospin chain is examined in terms of a finite-size Heisenberg spin Hamiltonian. One of the two kinds of spin sites in the chain represents an organic molecule with two S = 1/2 spins. The two spins interact antiferromagnetically to give a biradical molecule with a singlet (S = 0) ground state, which is coupled with adjacent S = 1/2 molecules by the intermolecular antiferromagnetic interactions. It is shown that S = 0 is not a good quantum number for describing the biradical embedded in the exchange-coupled chain and that the chain has a ferrimagnetic ground state with S = N/2 (N = the number of repeating units) or a low-spin state of S = 1/2 or S = 0, depending on the ratios of the intra- and intermolecular interactions. An extremely short spin-spin correlation length features in the low-spin state, indicating the occurrence of a quantum mechanical disorder resulting from a frustration effect inherent in the chain. The generalized ferrimagnetic spin alignment proposed in quantum terms uncovers a new category of molecule-based magnetic materials.