We investigate the copolymerization behavior of a two-component system into quasilinear self-assemblies under conditions that interspecies binding is favored over identical species binding. The theoretical framework is based on a coarse-grained self-assembled Ising model with nearest neighbor interactions. In Ising language, such conditions correspond to the antiferromagnetic case giving rise to copolymers with predominantly alternating configurations. In the strong coupling limit, we show that the maximum fraction of polymerized material and the average length of strictly alternating copolymers depend on the stoichiometric ratio and the activation free energy of the more abundant species. They are substantially reduced when the stoichiometric ratio noticeably differs from unity. Moreover, for stoichiometric ratios close to unity, the copolymerization critical concentration is remarkably lower than the homopolymerization critical concentration of either species. We further analyze the polymerization behavior for a finite and negative coupling constant and characterize the composition of supramolecular copolymers. Our theoretical insights rationalize experimental results of supramolecular polymerization of oppositely charged monomeric species in aqueous solutions.