Linear styrene-block-butadiene-block-styrene (SBS) triblock copolymers having different interfacial structures were investigated. In spite of the nearly equivalent chemical composition (about 70 vol% of styrene), these copolymers show significantly different morphologies. It was shown that the origin of the modified morphology in asymmetric block copolymers is the intermixing of short polystyrene (PS) chains or chain segments into the polybutadiene (PB) phase. It has a consequence of an increase in the glass transition temperature of the soft phase (PB phase here) and a significant decrease of the whole relaxation time of the materials. The larger the interfacial volume, the more PS molecules can mix into the PB phase. Moreover, it seems that the extent of the stress transfer in heterogeneous polymeric systems is crucially influenced by the interface. The tapered interface in an SBS block copolymer, for example, permits a more effective stress transfer compared to the sharp interface resulting in a higher degree of orientation in the individual phases of the materials.