A systematic numerical study of a minimalist model of conformationally and interaction asymmetric model binary blends has been carried out based on a computationally convenient formulation of PRISM theory and the free energy route to the thermodynamics. Effective chi-parameters based on the correlated enthalpic contribution to the free energy of mixing are computed within a constant volume and conformationally ideal description. The model calculations are carried out for molecular parameters which span the plausible range for hydrocarbon materials such as the polyolefins. Distinct regimes of miscibility behavior are found depending on whether the conformational and interaction asymmetries reinforce or tend to compensate. The former case is the most common experimental situation, and large positive chi-parameters are predicted due to the nonadditive influence of unfavorable bare energetic interactions and local packing differences between the stiffness asymmetric species. The theory predicts many non-mean-fieid behaviors observed in recent experiments such as failure of naive group contribution schemes, strong deuteration swap effects for random copolymer alloys, breakdown of the random copolymer theory for the effect of copolymer composition, and the possibility of unusual temperature dependences of, and apparent entropic contribution to, the effective X-parameter. if the conformational and interaction asymmetries tend to anticorrelate or compensate, then the theory predicts the possibility of negative chi-parameters associated with blend composition-dependent local packing rearrangements. This novel feature suggests several design strategies for achieving miscible high molecular weight polyolefin blends by rationally manipulating conformational and dispersion force properties of the polymer molecules. The blend theory is also compared with a microscopic version of a pure component-based solubility parameter theory. Overall, a remarkable agreement is found in the asymmetry reinforcement regime, but significant mixing "irregularities" can occur especially in the asymmetry compensation regime.