In the new era, the demand of bandwidth hungry applications is increasing day by day. In the similar manner, it is going to be unfeasible for the electromagnetic spectrum to adjust the latest broadband channels. Free-space optical (FSO) communication is one of the most dominant optical wireless communication (OWC) systems which not only provides the huge bandwidth, it provides licence-free spectrum as well. The FSO link connectivity problems due to the varying nature of weather can be overcome by using a parallel radio channel to the FSO. A hybrid optical/radio communication system is proposed with the assumption of Gamma-Gamma fading distribution for the FSO and Rician distribution for the radio channel. The proposed communication system is optimized by maximizing the total mutual information (MI) under all weather conditions (e.g., rain, fog and cloud). The optimization is done over the modulation and the joint power. The mapping schemes of the respective channel are optimally selected to maximize the MI while allocating the optimum power to each channel. Simulation results show that the proposed system always provides best MI under varying weather, i.e., both for the FSO and radio channel.