Differential scanning calorimetry (DSC), small-angle neutron scattering (SANS), and X-ray scattering (SAXS) have been used to investigate the solid-state morphology of blends of linear (high density) and long-chain-branched (low-density) polyethylenes (HDPE/LDPE). The blends are homogeneous in the melt, as previously demonstrated by SANS using the contrast obtained by deuterating the linear polymer. However, due to the structural and melting point differences (similar to 20 degrees C) between HDPE and LDPE, the components may phase segregate on slow cooling (0.75 degrees C/min). For high concentrations (phi greater than or equal to 0.5) of HDPE, relatively high rates of crystallization of the linear component lead to the formation of separate stacks of HDPE and LDPE lamellae, as indicated by two-peak SAXS curves. For predominantly branched blends, the difference in crystallization rate of the components becomes smaller and only one SAXS peak is observed, indicating that the two species are in the same lamellar stack. Moreover, the phases no longer consist of the pure components and the HDPE lamellae contain up to 15-20% LDPE (and vice versa). Rapid quenching into dry ice/2-propanol (-78 degrees C) produces only one SAXS peak (and hence one lamellar stack) over the whole concentration range. The blends show extensive cocrystallization, along with a tendency for the branched material to be preferentially located in the amorphous interlamellar regions. For high concentrations (phi > 0.5) of HDPE-D, the overall scattering length density (SLD) is high and the excess concentration of LDPE between the lamellae enhances the SLD contrast between the crystalline and amorphous phases. Thus, the interlamellar spacing (long period) is clearly visible in the SANS pattern. The blend morphology is a strong function of the quenching rate, and samples quenched less rapidly (e.g., into water at 23 degrees C) are similar to slowly cot!ed blends. The combination of SANS, SAXS, and DSC techniques allows us to interpret morphological differences in the solid state of these blends.