In this paper, the throughput performance of a hybrid Multiple-Input-Multiple-Output (MIMO) interweave/underlay Cognitive Radio (CR) system is examined on an analytical basis. Specifically, hybrid CR systems that switch between an interweave and an underlay transmission strategy, based upon spectrum sensing measurements, are investigated. For the first time the performance of such a hybrid CR system is analytically examined by deriving novel closed form approximations for the average achievable rate of the secondary system, as well as for the outage probability of the primary system. Capitalizing on the derived expressions, a new optimization problem for determining the sensing parameters, such as to maximize the average achievable rate of the secondary system, for a given outage probability of primary communication, is formulated and solved. The performance of the hybrid CR system is compared to the one achieved by the two conventional CR approaches and significant throughput gains are reported.