The development of bicontinuous morphologies in 10wt% polysulfone (PSu)–epoxy (DGEBA)/anhydride (MTHPA) blends, was followed by optical and scanning electron microscopy. Blends cured at 80°C revealed the formation of large epoxy-rich domains surrounded by a PSu-rich matrix, soon after the cloud point. Advancing the cure led to an increase in the volume fraction and the coalescence of epoxy-rich domains. A bicontinuous primary morphology was thus generated. A secondary phase separation was observed in both primary phases from the very beginning of the phase-separation process. While spinodal demixing was clearly the mechanism by which the primary morphology was generated, nucleation-growth could be responsible of the secondary phase separation. Postcure steps produced a change in the composition of phases as revealed by DMA, and in the secondary morphology as observed by SEM. A postcure at 120°C led to a single Tg at 115°C with a small shoulder at higher temperatures. A postcure at 200°C led to a Tg at 108°C for the epoxy-rich phase and a Tg at 137°C for the PSu-rich phase. The partial purification of the thermoplastic phase produced a significant enhancement of toughness. KIC was increased from 0.65MPam1/2 for the neat thermoset to 1.10MPam1/2 for the blend postcured at 200°C.