This paper identifies and characterizes complex core-shell morphologies in thin films of a polybutadiene-block-poly( 2-vinyl pyridine)-block-poly(tert-butyl methacrylate) (BVT) triblock terpolymer. The spin-coated BVT film develops into two distinct microphase separated structures with thickness variation during solvent annealing in a well-controlled atmosphere of THF vapor. Cylinders parallel to the film plane are found in thinner terraces and featureless areas that are characteristic of the lying lamella phase, or disordered structures are found in thicker terraces. Underneath the surface, we found that these microphase separated structures exhibit core-shell morphologies, i.e. surface ablation revealed core-shell cylinders and core-shell perforated lamellae under a cover layer in each terrace. Time-resolved study upon solvent annealing shows that the dynamics of microdomain evolution are affected by the extent of annealing time. The structural development in the BVT terpolymer films on corrugated supports demonstrates flow-field-induced sequenced ordering of the microdomains.