Chemical diffusion through boundaries involving two charged diffusing species (e.g., O2- and 2e(-) in an oxide) is modeled taking into account Poisson＇s equation, restricted to dilute systems and small driving forces. The results are compared with conventional treatments on a single crystal. Grain boundary effects are exemplified for (i) a bicrystal containing a grain boundary with adjacent space-charge layers and (ii) a polycrystal involving space-charge-free amorphous grain boundaries. Numerical results (i) are analyzed in the context of recent experiments on a SrTiO3 bicrystal. Transmission-line approximations for chemical diffusion in polycrystals are proposed and briefly compared with exact results.