Small-angle neutron scattering (SANS) was used to probe the thermodynamic interactions in multicomponent polymer blends including ternary blends containing two homopolymers and a block copolymer, mixtures of a homopolymer and a block copolymer, and a blend of two block copolymers. The polymers used for this study were model polyolefins-poly(ethylbutylene) and poly(methylbutylene) homopolymers and a poly(ethylbutylene)-block-poly(methylbutylene) copolymer. SANS profiles from homogeneous blends were measured over a wide range of blend composition, component molecular weights, and temperature. The Flory-Huggins interaction parameters, chi, in multicomponent mixtures were obtained from comparisons between the SANS data and theoretical predictions based on the multicomponent random phase approximation (RPA). At all temperatures, the multicomponent chi parameters were independent of blend composition, molecular weight and molecular architecture of the components. They were thus within experimental error of those obtained from binary homopolymer blends. All our measurements on this system are in agreement with the Flory-Huggins theory of polymer blends.