Dual-function radar-communication (DFRC) can alleviate spectrum congestion and competition with the spectrum-sharing architecture for next-generation wireless networks. In this article, we consider the problem of robust beamforming in millimeter wave (mmWave) DFRC systems. Unlike most existing works which assume that the angle-of-arrival (AoA)/angle-of-departure (AoD) or channel state information (CSI) is perfectly known, we consider the case of imperfect CSI resulting from the movement of users/targets or the beam misalignment errors. Our object is to maximize the achievable ergodic rate for communication under the constrained worst-case sensing signal-clutter-noise ratio (SCNR) for radar. By integrating the two-phase-shifter structure into our proposed robust hybrid beamforming architecture, it substantially improves the system performance and increases the design flexibility at the cost of doubling the number of phase shifters. With the two-phase-shifter structure, our proposed robust multibeam technology coherently combines sensing subbeams and communication subbeams with a widebeam radiation pattern for alleviating the effect of AoA/AoD uncertainty. Our proposed robust multibeam beamformer can shape the transmit waveform flexibly with very low complexity, which is amiable for practical implementation. Theoretical and numerical results validate the effectiveness and robustness of our proposed method in mmWave DFRC systems.