The effects of additive styrene/ethylene-butylene/styrene copolymer grafted with maleic anhydride (SEBS-g-MA) were investigated on the rheology, morphology and mechanical properties of a polyethylene terephthalate (PET)/high density polyethylene (HDPE) blend. The ratio of the two components was changed in small increments to track phase inversion. The rheology measurements show that SEBS-g-MA acts differently on HDPE and PET, as different morphologies are formed due to viscosity ratio change. With the help of electron microscopy various phases after extrusion and after injection molding were revealed and identified. Because of the high viscosity of HDPE the co-continuous morphology was immediately formed when PET reached 30 vol%. The range of the co-continuous structure of the blend was wider when SEBS-g-MA was added, and the elongation at break also improved as additive content increased, without a significant strength decrease. The divergence of the mechanical properties from the theoretical value, i. e. the value determined by the mixing rule, can be explained by the changing phase structure.