This study discusses the integrated system of full‐duplex (FD) multiple‐input‐multiple‐output (MIMO) communication and MIMO radar, which has been rarely considered in published studies. Such an integrated system is composed of a base station and several uplink (UL) and downlink (DL) users, and is supposed to simultaneously implement three functionalities, that is, target detection, UL and DL communications. The degrees of freedom of system design involve the precoding and combining schemes for UL and DL communications, as well as the receiving filter for radar echo. An optimization problem is developed to maximise a compound communication sum‐rate metric subject to the SINR constraint imposed on target detection performance. The resulted non‐convex and NP‐hard problem is first divided into two sub‐problems. Then, for one of the sub‐problems that is still intractable, its solution is iteratively obtained based on the fractional programing technique and the consensus alternating direction method of multipliers algorithm. In the simulation part, the convergence performance and computational efficiency of the proposed algorithm are illustrated. In addition, the target detection performance, DL and UL communication performance of the integrated system are also evaluated.