In this paper, we propose a novel architecture for hybrid radio frequency (RF)/free-space optics (FSO) wireless systems. In particular, we show that a hybrid system robust to all weather conditions is obtained by joint bit-interleaved coded modulation (BICM) of the bit steams transmitted over the RF and FSO sub-channels. An asymptotic performance analysis reveals that a properly designed convolutional code can exploit the diversity offered by the independent sub-channels. Furthermore, we develop a code design criterion and provide an efficient code search procedure. Simulation results show that hybrid RF/FSO systems with BICM outperform previously proposed hybrid systems employing a simple repetition code and selection diversity.