Structure self-assembling in the late stage spinodal decomposition of a polymer blend at its critical composition has been explored by laser-scanning confocal microscopy with particular emphasis on the effects of confinement (dimensionality) and preferential wetting of solid surface by one of the constituent polymers. A mixture of deuterated polybutadiene and polybutadiene (PB) with relatively narrow thickness (D congruent with 55 microm) was observed in three dimensions over the entire thickness. Formation of a wetting layer was clearly observed near the glass surface, while a bicontinuous structure evolved in the middle of the specimen. Global as well as local features of the phase-separating structures were quantified by several structural parameters, e.g., characteristic length Lambda(m)(t), structure factor S(q), interfacial area per unit volume Sigma(t), probability densities of interfacial curvatures P(H,K;t), etc. (t is a phase-separation time). From the time evolution of these structural parameters, a deviation from the self-similar growth of a bicontinuous structure was found to occur at a transition time, t(tr), at which a scaled thickness, D/Lambda(m), approached unity. The breakdown of the self-similar growth was most sensitively observed by the local characteristics, i.e., Sigma(t) and P(H,K;t). On the other hand, the global characteristic, Lambda(m)(t), did not provide useful insight into the effects of dimensionality. It turned out that the bicontinuous structure, initially growing with dynamical self-similarity, eventually transformed into a "columnlike" structure (at t congruent with t(tr)) in which cylindrical PB-rich domains bridge the upper and lower PB wetting layers.