In communication networks, where users are highly mobile, migrating edge servers that are performing services closer to users, i.e., service migration, is essential to maintain the high quality of service (QoS). However, existing dynamic service migration techniques face two distinct challenges: (1) The security and energy consumption of service migration systems need to be optimised urgently; (2) The uncertainty of user movement makes it difficult to develop optimal service migration strategies, especially in future three-dimensional (3-D) communication networks. To address these challenges, we propose a novel energy-efficient secure 3-D dynamic service migration framework for communication networks. We then quantify the cost of service migration based on the proposed framework considering security, energy efficiency and delay and present a solution based on a deep reinforcement learning (DRL) approach to make migration decisions optimally in the 3-D communication network. We also propose a universal formula for measuring the reliability value of intelligent autonomous nodes in order to reduce the energy consumption and delay of the proposed security paradigm and to optimise the service migration decision making. Simulation results demonstrate our proposed migration strategy for 3-D communication network services outperforms the baseline solutions in terms of reducing communication network delay and energy consumption while preserving migration security. Moreover, the results confirm the effectiveness of the proposed reliability value calculation approach applied to improve the QoS in the secured edge networks.