Bilateral cochlear implants (CIs) greatly improve spatial hearing acuity for CI users, but substantial gaps still exist compared to normal-hearing listeners. For example, CI users have poorer localization skills, little or no binaural unmasking, and reduced spatial release from masking. Multiple factors have been identified that limit binaural hearing with CIs. These include degradation of cues due to the various sound processing stages, the viability of the electrode-neuron interface, impaired brainstem neurons, and deterioration in connectivity between different cortical layers. To help quantify the relative importance and inter-relationship between these factors, computer models can and arguably should be employed. While models exploring single stages are often in good agreement with selected experimental data, their combination often does not yield a comprehensive and accurate simulation of perception. Here, we combine information from CI sound processing with computational auditory model stages in a modular and open-source framework, resembling an artificial bilateral CI user. The main stages are (a) binaural signal generation with optional head-related impulse response filtering, (b) generic CI sound processing not restricted to a specific manufacturer, (c) electrode-to-neuron transmission, (d) binaural interaction, and (e) a decision model. The function and the outputs of different model stages are demonstrated with examples of localization experiments. However, the model framework is not tailored to a specific dataset. It offers a selection of sound coding strategies and allows for third-party model extensions or substitutions; thus, it is possible to employ the model for a wide range of binaural applications and even for educational purposes.