While numerous studies have investigated the effect of adding a block copolymer as a macromolecular surfactant to immiscible polymer blends, no such efforts have sought to alter the properties of melt-spun bicomponent core-sheath filaments with a nonreactive compatibilizing agent. In this study, we examine the effect of adding poly[styrene-b-(ethylene-co-butylene)-b-styrene] (SEBS) triblock copolymer to core-sheath filaments consisting of isotactic poly-propylene (iPP) and poly(lactic acid) (PLA). Incorporation of the copolymer into blends of iPP/PLA is observed to reduce the size scale of phase separation. Interfacial slip between molten iPP and PLA layers is evaluated by rheology under steady-shear conditions. Addition of SEBS to the PLA sheath during filament formation reduces the tendency of PLA sheaths to crack prior to iPP core failure during tensile testing. In reversed filament configurations, the copolymer does not hinder the development of molecular orientation, related to fiber strength, during fiber spinning. Electron microscopy reveals that the copolymer molecules form unique, highly nonequilibrium morphologies under the spinning conditions employed here.