A system consisting of polyethylene blended with a branched ethylene/ethyl acrylate (EEA) copolymer (18 wt % EA) is studied by the technique of neutron scattering. We find that an analysis using the two-parameter Debye-Bueche model allows determination of blend morphology both above and below the melt temperature. Above the melt temperature, this blend is inhomogeneous at all compositions, with the EA groups within the copolymer associating on length scales of approximately 30-40 Angstrom. Below the melt temperature, we determine the thicknesses of the polyethylene crystalline (delta(c)) and amorphous (delta(a)) regions, finding delta(c) = 140 Angstrom and delta(a) = 110 Angstrom with little variation with composition or temperature. Finally, we determine the structure of the blend during the melt-crystalline transition, allowing us to gain insight into the crystalline phase growth mechanism.