Bicontinuous morphologies constitute an exciting new genre of microstructure in microphase-separated block copolymers and have thus far been observed in neat poly(styrene-b-isoprene) (SI) diblock and star-block copolymers, as well as in binary copolymer/homopolymer and copolymer/copolymer blends. While diblock and star-block copolymers differ in their molecular architectures, they both possess terminal (outer) blocks composed of a single monomer species. These terminal blocks are anchored at one end (the block junction) and unconstrained at the other. In the present work, linear (SI)n multiblock copolymers which consist of n (2 less-than-or-equal-to n less-than-or-equal-to 4) perfectly-alternating SI block pairs are blended with homopolystyrene (hPS). The conditions under which these blends are prepared are identical to those used to generate the ordered bicontinuous double-diamond (OBDD) morphology in (SI)1/hPS blends. Transmission electron microscopy (TEM) reveals, however, that none of the blends produced here exhibit this morphology. In some cases, hPS is solubilized within the copolymer microstructure, resulting in either dispersed isoprene cylinders or swollen lamellae. Macrophase separation also occurs, depending on copolymer architecture and block length. The morphologies observed in this work are interpreted in terms of the conformational behavior of linear multiblock copolymers and competition between microphase ordering and macrophase separation.