Side-chain liquid-crystalline-b-amorphous copolymers combine the thermotropic ordering of liquid crystals (LCs) with the physics of block copolymer phase segregation. In our earlier experiments, we observed that block copolymer order-order and order-disorder transitions could be induced by LC transitions. Here we report the development of a free-energy model to understand the interplay between LC ordering and block copolymer morphology in an incompressible melt. The model considers the interaction between LC moieties, the stretching of amorphous chains from curved interfaces, interfacial surface contributions, and elastic deformation of the nematic phase. The LC block is modeled with Wang and Warner's theory, in which nematogens interact through mean-field potentials, and the LC backbone is modeled as a wormlike chain. Free energy is estimated for various morphologies: homogeneous, lamellar, cylinder micelle, and spherical micelle. Phase diagrams were constructed by iteration over temperature and composition ranges. The resulting composition diagrams are highly asymmetric, and a variety of first-order transitions are predicted to occur at the LC clearing temperature. Qualitatively, nematic deformation energies destabilize curved morphologies, especially when the LC block is in the center of the block copolymer micelle. The thermodynamics of diblocks with laterally attached, side-on mesogens are also explored. Discussion focuses on how well the model captures experimental phenomena and how the predicted phase boundaries are affected by changes in polymer architecture.