Effective diffusivity through heterogeneous media containing impermeable and geometrically anisotropic domains depends on the domain orientation relative to the diffusion direction. A particular class of heterogeneous membranes in which domain orientation can be controlled in situ, side-chain liquid-crystalline polymers (SCLCPs), are being investigated as responsive, or variable permeability membranes for use in a variety of applications including controlled release drug delivery. This paper describes a geometric model for predicting the effective diffusivity through this type of membranes as a function of domain orientation, volume fraction, and aspect ratio. Estimates of effective diffusivity were also generated using random walk simulations. Results from the two methods agree well with each other. Predicted effective diffusivities in systems with domains aligned either orthogonal or parallel to the diffusion direction are compared to results from available literature models. Model predictions are compared to experimentally obtained transport properties through SCLCPs in which liquid-crystalline domain orientation is modulated by externally applied electric field.