The phase behavior of ternary polymer blends comprising poly(cyclohexylethylene) (C) and polyethylene (E) homopolymers and a compositionally asymmetric CE diblock copolymer with f(c) = 0.67 was investigated, where f(c) is the volume fraction of C. The morphology was established in the phase prism (volume fractions of C, E, and CE vs temperature) by optical transmission, small-angle X-ray scattering, and small-angle neutron scattering measurements. The locations of lamellar (LAM), hexagonally packed cylinders and gyroid ordered phases are shifted significantly toward lower fractions of the C homopolymer compared to previous results obtained from ternary polymer blends with a symmetric diblock copolymer (f(c) = 0.5). Conversely, the Scott line of critical points, which delineates the boundary between single-phase disorder and macroscopic phase separation, remains virtually unchanged, coincident with the fraction of the C homopolymer associated with the binary homopolymer blend critical composition. A central finding of this study is that the line of nearly congruent order-disorder transitions, where the LAM phase melts virtually directly into the disordered state, is decoupled in composition from that of the Scott line of critical points. A wide range of phase space between the compositions associated with the congruent transition and Scott line was identified as containing a microemulsion morphology. This study demonstrates that diblock copolymer compositional asymmetry significantly impacts the ordered phase regime but has a marginal effect on the region displaying macroscopic phase separation. It also provides useful guidance for tuning the interfacial curvature, a crucial factor in the formation of bicontinuous microemulsions.