The samples of the polystyrene-polybutadiene (PSPB) diblock copolymers with lamellar structure were investigated by integral and partial thermally stimulated depolarization current (TSDC) measurements in the 160-303 K range, and compared to the analogous investigation performed on a homopolymer sample of polystyrene (PS), The current peak, which appeared at 187 K, was found to be a dipolar relaxation oi peak caused by the glass transition in the PB phase. The space-charge relaxation, distributed in the 220-260 K range and split into two parts - denoted as beta(1) and beta(2), was attributed to the possible local motion of the phenyl rings in the PS phase. The current maxima of the beta relaxations significantly increased and shifted to the lower temperatures in the copolymer samples due to the PS-PB interfaces. The occurrence of doubleness and the relative distance between beta(1) and beta(2) was discussed. The relative numbers of the relaxing dipoles (N) vs. E-a were approximated. The energy width (omega) was significantly increased in the copolymers due to the released motions at the glass-liquid PS-PB interfaces.