We present extensive simulations modeling the casting of multiblock polymer films by evaporation. The domain structure of the resulting film is strongly affected by varying the relative stiffness of the coblocks. The morphology changes from a bicontinuous lamellar phase when both blocks are flexible to a small-scale phase-separated phase with isolated domains as the stiffness of one of the blocks increases. As the relative stiffness of the blocks changes, the rate of evaporation, interfacial width, and morphology of the system changes. The findings can be used to tailor membrane morphology of interest to fuel-cell applications where the morphology is important for proton conduction.