Multi-cell wireless systems usually suffer both intra-cell and inter-cell interference, which can be mitigated via coordinated multipoint (CoMP) techniques. Previous works on multi-cell analysis for the microwave band generally consider fully digital beamforming that requires a complete radio-frequency chain behind each antenna, which is less practical for millimeter-wave (mmWave) systems where large amounts of antennas are necessary to provide sufficient beamforming gain and to enable transmission and reception of multiple data streams per user. This paper proposes four analog and digital hybrid beamforming schemes for multi-cell multi-user multi-stream mmWave communication, leveraging CoMP. Spectral efficiency performances of the proposed hybrid beamforming approaches are investigated and compared using both the 3rd Generation Partnership Project and NYUSIM channel models. Simulation results show that CoMP based on maximizing signal-to-leakage-plus-noise ratio can improve spectral efficiency as compared to the no-coordination case, and spectral efficiency gaps between different beamforming approaches depend on the interference level that is influenced by the cell radius and the number of users per cell.