This paper examines binary blends of homopolymer with diblock copolymer, using numerical self-consistent field (NSCF) theory. On the basis of the general formalism, we identify the minimum number of characteristics of a blend needed to predict its equilibrium morphology and domain sizes. We then specialize to the case of A homopolymer added to A-b-B copolymer and carry out a series of NSCF calculations of the effects of solubilized homopolymer and its distribution throughout each domain. We present a detailed analysis of when the added homopolymer induces an increase or decrease in the domain thickness, compare strong and weak segregation behavior, identify the dominant controlling characteristics and the underlying physics, and make quantitative comparison with experiment. Many of the results are captured in a simple equation. We also suggest a procedure for determining X parameters.