We investigate the influence of an asymmetric PS-b-PMMA block copolymer (bcp) on the morphology of melt-mixed immiscible binary polymer blends containing poly(styrene-co-acrylonitrile) random copolymer (SAN) and poly(cyclohexylmethacrylate) (PCHMA). By varying the SAN copolymer composition, the balance between the swelling of each block segment located at the interface between the two phases is altered and the effect on blend morphology is studied. As in earlier studies using a symmetric bcp, we find that for a specified shear history, there is a zone of effective emulsification of the blend bounded by regions of internal and external emulsification failure. However, the locations of the boundaries between stable and unstable emulsification differ for an asymmetric versus a symmetric bcp. Thus the morphology depends not only on the segmental swelling ratio but also on the difference in the effective size of each bcp segment. Scaling arguments successfully correlate the limits of stable emulsification for both symmetric and asymmetric bcp.