This paper describes a study of thermodynamic interactions in binary blends of AyB1-y copolymers. The blend components are hydrogenated polybutadienes, consisting of chains with branched C4 and linear C4 units and corresponding to model ethylene-butene copolymers. Overall compositions range from nearly polyethylene (y = O) to nearly poly(butene-1) (y = 1) through a series of nearly random branched C4-linear C4 copolymers. Values of the Flory-Huggins interaction parameter chi were determined by small-angle neutron scattering (SANS) from binary blends (one component deuterated) and then corrected for the effect of isotopic substitution. The reduced interaction parameter chi/y2 - y1)2 was found to be a strong function of the average blend composition, contrary to classical copolymer theory. Higher order theories, based on diad or triad interactions, could be made to fit, but the physical significance of the fits was unclear. The same results were also expressed in terms of a relative solubility parameter, delta - delta(ref), for each copolymer. These values were found to agree well with calculations based on PVT properties of the pure components. Thus, it seems clear that, for this system at least, departures from the copolymer equation are foretold in the pure component properties and have nothing to do with anomalies associated with mixing. More generally, inferences about the mixing process that are based on the temperature dependence of chi alone must be viewed with great caution.