We present a small-angle X-ray scattering (SAXS) and wide-angle X-ray scattering (WAXS) characterization of the semicrystalline structure of homo- and heterobicomponent core-sheath fibers melt-spun from poly(ethylene terephthalate) (PET) and poly(phenylene sulfide) (PPS). The two-dimensional SAXS/WAXS patterns of the various bicomponent fibers are found to reflect the mutual influence of the components on their thermal profiles along the spinline, leading to modified crystallization of the PET component and a larger strain rate in the PPS component. The predominant scattering features in the SAXS patterns are four-point reflections, an intense equatorial streak, and a central anisotropic diffuse scattering. The four-point reflections are attributed to tilted crystalline lamellar stacks of PET. The lamellar stack dimensions and the orientation of their lamellar surfaces are determined. We find that the heterobicomponent arrangement can promote the formation of equally spaced and uniformly sized crystallites in the PET phase and highly oriented crystallites in the PPS phase.