In the context of integrated sensing and communication (ISAC), a full-duplex (FD) transceiver can operate as a monostatic radar while maintaining communication capabilities. This paper investigates the design of precoders and combiners for a joint radar and communication (JRC) system at mmWave frequencies. The primary goal of the design is to guarantee certain performance in terms of some sensing and communication metrics while minimizing the self-interference (SI) caused by FD operation and taking into account the hardware limitations coming from a hybrid MIMO architecture. Specifically, we introduce a generalized eigenvalue-based precoder design that considers the downlink user rate, the radar gain, and the SI suppression. Since the hybrid analog/digital architecture degrades the SI mitigation capability of the precoder, we further enhance SI suppression with the analog combiner. Our numerical results demonstrate that the proposed architecture achieves the required radar gain and SI mitigation while incurring a small loss in downlink spectral efficiency. Additionally, the numerical experiments also show that the use of orthogonal frequency division multiplexing (OFDM) radar with the proposed beamforming architecture results in highly accurate range and velocity estimates for the detected targets.