This paper presents an investigation of the performance of a reconfigurable intelligent surface (RIS)-assisted free-space optical (FSO)/radio frequency (RF) hybrid system by considering the effect of the cochannel interference problem in the RF link. An RIS is used to address the inability of the RF link to complete line-of-sight communication and thus improve the communication system performance. The FSO link adheres to a double generalized gamma distribution and considers the pointing error effect, while the RF link obeys a Rayleigh distribution. Further, a decode-and-forward protocol is used at the relay node to mitigate noise interference in the transmitted signal. The cumulative distribution function of the end-to-end instantaneous signal-to-noise ratio of the system is then derived; on this basis, the closed formulas for the outage probability and average bit error rate (BER) of the system are derived. The simulation results show that the performance improvement of this system scheme is relatively evident under weak and medium turbulence intensity. Under weak turbulence intensity, the RIS can effectively resist the influence of interference on the RF link, thus improving the system performance.