In this study, a drift-diffusion model is used to derive the current-voltage curves of an organic bilayer solar cell consisting of slabs of electron acceptor and electron donor materials sandwiched together between current collectors. A simplified version of the standard drift-diffusion equations is employed in which minority carrier densities are neglected. This is justified by the large disparities in electron affinity and ionisation potential between the two materials. The resulting equations are solved (via both asymptotic and numerical techniques) in conjunction with (i) Ohmic boundary conditions on the contacts and (ii) an internal boundary condition, imposed on the interface between the two materials, that accounts for charge pair generation (resulting from the dissociation of excitons) and charge pair recombination. Current-voltage curves are calculated from the solution to this model as a function of the strength of the solar charge generation. In the physically relevant power generating regime, it is shown that these current-voltage curves are well-approximated by a Shockley equivalent circuit model. Furthermore, since our drift-diffusion model is predictive, it can be used to directly calculate equivalent circuit parameters from the material parameters of the device.