Combining a cochlear implant with contralateral acoustic hearing typically enhances speech understanding, although this improvement varies among CI users and can lead to an interference effect. This variability may be associated with the effectiveness of the integration between electric and acoustic stimulation, which might be affected by the temporal mismatch between the two listening sides. Finding methods to compensate for the temporal mismatch might contribute to the optimal adjustment of bimodal devices and to improve hearing in CI users with contralateral acoustic hearing. The current study investigates cortical auditory evoked potentials (CAEPs) in normal hearing listeners (NH) and CI users with contralateral acoustic hearing. In NH, the amplitude of the N1 peak and the maximum phase locking value (PLV) were analyzed under monaural, binaural, and binaural temporally mismatched conditions. In CI users, CAEPs were measured when listening with CI only (CIS_only), acoustically only (AS_only) and with both sides together (CIS+AS). When listening with CIS+AS, various interaural delays were introduced between the electric and acoustic stimuli. In NH listeners, interaural temporal mismatch resulted in decreased N1 amplitude and PLV. Moreover, PLV is suggested as a more sensitive measure to investigate the integration of information between the two listening sides. CI users showed varied N1 latencies between the AS_only and CIS_only listening conditions, with increased N1 amplitude when the temporal mismatch was compensated. A tendency towards increased PLV was also observed, however, to a lesser extent than in NH listeners, suggesting a limited integration between electric and acoustic stimulation. This work highlights the potential of CAEPs measurement to investigate cortical processing of the information between two listening sides in NH and bimodal CI users.