Styrene-block-butadiene-block-styrene (SBS) triblock copolymer epoxidized with 47 mol % degree of epoxidation (eSBS47) by hydrogen peroxide in a water/dichloroethane biphasic system was blended with epoxy based on diglycidyl ether of bisphenol A (DGEBA) and 4,4'-diaminodiphenylmethane (DDM) as a curing agent. The amounts of eSBS in the blends were 10 and 20 wt %. The evolution of the glass transition temperatures (T-g) of the cured blends at different cure times was analyzed using differential scanning calorimetry (DSC) to understand the thermal behavior of epoxy system under dynamic conditions in the presence of eSBS. Transmission electron microscopy (TEM) analysis revealed core shell nanodomains of eSBS dispersed in the epoxy matrix. The relationship between rheology and phase separation was carefully explored. Dynamic mechanical analysis (DMA) validated the nanophase-separated structure of the eSBS47-modified epoxy system. Upon addition of eSBS47 to the epoxy system, the fracture toughness of the nanostructured thermosets was improved, and the thermal stability was retained, but the dimensional stability was slightly decreased.