Bilateral cochlear implant (BICI) listeners do not have full access to the binaural cues that normal hearing (NH) listeners use for spatial hearing tasks such as localization. When using their unsynchronized everyday processors, BICI listeners demonstrate sensitivity to interaural level differences (ILDs) in the envelopes of sounds, but interaural time differences (ITDs) are less reliably available. It is unclear how BICI listeners use combinations of ILDs and envelope ITDs, and how much each cue contributes to perceived sound location. The CCi-MOBILE is a bilaterally synchronized research processor with the untested potential to provide spatial cues to BICI listeners. In the present study, the CCi-MOBILE was used to measure the ability of BICI listeners to perceive lateralized sound sources when single pairs of electrodes were presented amplitude-modulated stimuli with combinations of ILDs and envelope ITDs. Young NH listeners were also tested using amplitude-modulated high-frequency tones. A cue weighting analysis with six BICI and ten NH listeners revealed that ILDs contributed more than envelope ITDs to lateralization for both groups. Moreover, envelope ITDs contributed to lateralization for NH listeners but had negligible contribution for BICI listeners. These results suggest that the CCi-MOBILE is suitable for binaural testing and developing bilateral processing strategies.