In this paper, we present and analyze a new transmission scheme for hybrid FSO/RF communication system based on joint adaptive modulation and adaptive combining. Specifically, the data rate on the FSO link is adjusted in discrete manner according to the FSO link's instantaneous received signal-to-noise-ratio (SNR). If the FSO link's quality is too poor to maintain the target bit-error-rate, the system activates the RF link along with the FSO link. When the RF link is activated, simultaneous transmission of the same modulated data takes place on both links, where the received signals from both links are combined using maximal ratio combining scheme. In this case, the data rate of the system is adjusted according to the instantaneous combined SNRs. Novel analytical expression for the cumulative distribution function (CDF) of the received SNR for the proposed adaptive hybrid system is obtained. This CDF expression is used to study the spectral and outage performances of the proposed adaptive hybrid FSO/RF system. Numerical examples are presented to compare the performance of the proposed adaptive hybrid FSO/RF system with that of switch-over hybrid FSO/RF and FSO-only systems employing the same adaptive modulation schemes.