Visible light communication (VLC) is an effective alternative technology to overcome the limitations related to the radio frequency (RF) spectrum. In the modern day of communication systems, the energy harvesting (EH) technique is considered as a promising technology to design more energy efficient communication systems. Integrating VLC with the EH technology in wireless networks guaranties the reliability of these networks. In this paper, we consider a dual-hop VLC/RF wireless communication, composed of two Light Emitting Diodes (LEDs) and two receivers, assisted by a decode-And-forward (DF) relaying system operating with EH in order to boost the coverage of VLC systems. Using successive interference cancellation, we derive achievable rates of both users. Afterwards, we determine the achievable rate-region for this communication system where we show that this region can take four shapes depending on the communication scenario. Then, we formulate the achievable rate-region maximization problem, and we develop solution to find the optimal design for the EH time switching protocol. Further, we show that EH enhances the performance of the communication system in a certain regime of its initial power. We finally present selected numerical result to verify the analytic results.