By performing a series of experiments on a thermoset/thermoplastic blend of epoxy/polyarylsulfone thermoplastic we are able to characterize many important parameters of the components and their interactions. We pay particular attention to the competition between phase separation and cross-linking of the epoxy, which makes these systems technologically important but complex. Using small-angle neutron scattering we determine an effective Flory-Huggins interaction parameter as a function of the temperature and the molecular weight distribution of each component, which is determined by gel permeation chromatography. These results are then incorporated into a recent model for linear/branched polymer blends to predict the evolution of phase diagrams under isothermal cure. Small-angle light scattering and scanning electron microscopy show morphologies in close agreement with the model.