Current-induced domain wall motion and magnetization dynamics in the CoFeB layer of CoFeB/Cu/Co nanostripes were studied using photoemission electron microscopy combined with x-ray magnetic circular dichroism (XMCD-PEEM). Quasi-static measurements show that current-induced domain wall motion in the CoFeB layer is similar to the one observed in the NiFe layer of NiFe/Cu/Co trilayers, although the threshold current densities for domain wall depinning are lower. Time-resolved XMCD-PEEM measurements are used as an efficient probe of domain wall depinning statistics. They also reveal that, during the application of current pulses, the CoFeB magnetization rotates in the direction transverse to the nanostripe. The corresponding tilt angles have been quantified and compared to analytical and micromagnetic calculations, highlighting the influence of magnetostatic interactions between the two magnetic layers on the magnetization rotation.