A Hybrid LiFi and WiFi network (HLWNet) integrates the rapid data transmission capabilities of Light Fidelity (LiFi) with the extensive connectivity provided by Wireless Fidelity (WiFi), resulting in significant benefits for wireless data transmissions in the designated area. However, the challenge of decision-making during the handover process in HLWNet is made more complex due to the specific characteristics of electromagnetic signals' line-of-sight transmission, resulting in a greater level of intricacy compared to previous heterogeneous networks. This research work addresses the problem of handover decisions in the Hybrid LiFi and WiFi networks and treats it as a binary classification problem. Consequently, it proposes a handover method based on a deep neural network (DNN). The comprehensive handover scheme incorporates two sets of neural networks (ANN and DNN) that utilize input factors such as channel quality and the mobility of users to enable informed decisions during handovers. Following training with labeled datasets, the neural-network-based handover approach achieves an accuracy rate exceeding 95%. A comparative analysis of the proposed scheme against the benchmark reveals that the proposed method considerably increases user throughput by approximately 18.58% to 38.5% while reducing the handover rate by approximately 55.21% to 67.15% compared to the benchmark artificial neural network (ANN); moreover, the proposed method demonstrates robustness in the face of variations in user mobility and channel conditions.