A LiFi-RF heterogeneous network can provide additional capacity to standalone wireless technologies due to their non-interfering nature. However, due to the properties of the short-range LiFi channel, the network is prone to transient channel variations that result in frequent, unnecessary handovers. This handover process creates an overhead and can result in the loss of connection. To ensure a stable connection for all users, a low complexity resource allocation algorithm, that considers the loss due to handovers, is proposed to minimize the number of handovers. This algorithmic approach is evaluated with simulations. For scenarios with unavoidable handovers, a system approach to manage vertical handovers is proposed to minimize the vertical handoff overhead and to offer a seamless interface switch, thereby resulting in a stable network. This protocol is implemented in hardware and the results show a negligible overhead.