We study a cooperative transmission scheme for a joint multiple-input-multiple-output (MIMO) radar and multi-user (MU) MIMO downlink communication system, where both systems operate on the same frequency band simultaneously. Maximization of the total weighted system mutual information or sum rate is considered with the presence of an extended target and environmental clutter. An alternating optimization based iterative algorithm is proposed to find the transmit covariance matrices for both radar and communication applications. A power allocation policy for the downlink communication is also developed through the same algorithm.