Microstructures of block copolymers in the strong segregation limit are characterized by well-defined interfaces separating the different block materials into domains on a nanometer scale. In this paper, we address the effects of architectural and conformational asymmetry of the blocks on the interfacial curvature characteristics and on the degree of long-range order in the cylindrical morphologies. Experimental (TEM and SAXS) curvature data from polyisoprene-polystyrene (I2S) simple graft block copolymers and from polyisoprene-poly(tert-butyl methacrylate) (PtBMA) linear, conformationally asymmetric diblock copolymers are presented and compared to data from polyisoprene-polystyrene linear diblock copolymers. The experimental data are elucidated by a simple curvature free energy model which accounts for core-space-filling without explicitly specifying the shape of the microdomain. This model allows the prediction of preferred interfacial curvature characteristics as a function of molecular architecture. Good agreement is obtained between the theoretically calculated mean and Gaussian curvatures and the experimentally measured values. A key finding is that the degree of frustration, as measured by the difference between the free energy of the preferred curvature of a given block copolymer and that of the nearest accessible space-filling structure (such as the cylindrical structure), is correlated with the degree of long-range order.