Three poly(styrene)-block-poly(isoprene)-block-poly(lactide) (PS-b-PI-b-PLA, SIL) triblock terpolymers were synthesized and characterized in the bulk and as thin films. The pronounced incompatibility of the covalently connected PI and PLA led to significant frustration and the tendency to minimize their intermaterial dividing surface area. This resulted in the formation of a core-shell cylinder morphology with exaggerated nonconstant mean curvature from triblock polymers with equal block volume fractions rather than the more typical lamellar morphology. The effect of frustration was magnified in thin films by both confinement and interfacial interactions such that the PI domains became discontinuous. Self consistent field theory (SCFT) calculations emphasize that the marked difference in the PS/PI and PI/PLA interaction parameters promotes the formation of nonlamellar morphologies. However, SCFT predicts that lamellar morphology is more stable than the observed cylindrical morphology, demonstrating a limitation that arises from the underlying assumptions.