Network coverage in high-altitude mountainous regions remains a persistent challenge, primarily due to complex terrain and severe signal attenuation. To enable effective signal detection in such environments, this paper addresses the critical need for robust path planning for unmanned aerial vehicles (UAVs) under multiple operational constraints. In this paper, we propose a Multi-objective Hybrid Mantis Search Algorithm (MHMSA) that optimizes UAV trajectories by integrating a comprehensive cost function encompassing UAV dynamic constraints, terrain-induced threats, energy consumption, and communication limitations. The algorithm incorporates three core strategies: coupled step size control for stable convergence, dynamic spiral search to enhance global exploration, and a fitness-distance balance (FDB) mechanism for optimal individual selection. These enhancements collectively improve optimization efficiency, path accuracy, and the ability to escape local optima. Extensive simulations in both synthetic multi-obstacle environments and a real-world digital elevation model (DEM) of the Qinling Mountains demonstrate the superior performance of MHMSA. Compared to the second-best benchmark algorithm, it achieves an average reduction of 3.5% in path length and 5.1% in comprehensive fitness value, confirming its advantages in both solution quality and convergence stability for UAV path planning in complex mountainous terrains.