Highly asymmetric block copolymers forming spherical microdomains arrange in a hexagonal lattice as a monolayer, while the bulk equilibrium structure is body-centered cubic. We report a complex transition from two- to three-dimensional packing in thin films of spherical-domain poly(styrene-b-2vinylpyridine), measured by grazing-incidence small-angle X-ray scattering and transmission electron microscopy. The monolayer hexagonal symmetry persists through three layers, with close-packed AB and ABA stacking in films two and three layers thick. At four layers, coexistence between an equilibrium hexagonal close-packed symmetry and a metastable face-centered orthorhombic structure is observed. As the number of layers is further increased from 4 to 23, the hexagonal phase vanishes, and the symmetry of the face-centered orthorhombic phase deforms to approach asymptotically a structure similar to a body-centered cubic lattice with the closest-packed (110) plane oriented parallel to the substrate. Self-consistent-field theory calculations demonstrate that these thickness-dependent packing symmetries result from a competition between the packing preferred in the bulk with that at the interfaces.(1)