This paper evaluates the secrecy outage probability of a hybrid radio frequency (RF) and visible light communication (VLC) network in the presence of an eavesdropper. We assume that data is transmitted over the RF and VLC links following a proposed multiplexing scheme in which the data sent by the source is split with a certain allocation ratio. Furthermore, the legitimate and eavesdropper users are assumed to have multihoming capabilities, so that they are able to receive data from both RF and VLC access points, simultaneously. We derive integral-form exact expression, as well as a closedform asymptotic expression for the secrecy outage probability and validate them via Monte Carlo simulations. Our results show that multiplexing the information signal by both links leads to an enhancement of the secrecy performance since it opportunistically takes advantages of the best characteristics of both domains.