In this work, we investigate the morphological and mechanical properties of blends of diglycidyl ether of bisphenol-A (DGEBA) and epoxidized polystyrene-polybutadiene star block copolymer (epST3) using diamino-diphenyl sulphone (DDS) as a hardener. The epoxidation of the star block copolymer was performed using meta-chloroperoxybenzoic acid (m-CPBA). Chemical modification of the copolymer was characterized by Fourier transform infrared (FTIR) spectroscopy while the morphology of the blends was analyzed by microscopic techniques. The mechanical behavior of the blends was analyzed by recording microindentation as well as impact tests. It has been demonstrated that the completely macrophase-separated morphology of the blends could be dispersed into the structures comprising co-continuous networks of the block copolymer phase and the epoxy resin leading to an increment in impact strength. At the same time, the hardness and stiffness of the blends, as shown by the indentation microhardness and indentation modulus, was maintained to a pretty high level.