We present a statistical mechanical approach for predicting the self-assembled morphologies of amphiphilic diblock copolymers in the melt. We introduce two conformationally asymmetric linear copolymer models with a local structural asymmetry, one of a "comb-tail'' type and another that we call "continuous jackknife model.'' The copolymers consist of amphiphilic and "monophilic'' (non-amphiphilic) blocks, which have different segmental volume and tend to segregate into subphases. Using a self-consistent field theory (SCFT) framework, we explore the phase diagrams for these copolymers and compare them with that known for conventional, conformationally symmetric diblock copolymers. To determine the impact of structural effects on the self-asse...