Max-pressure (MP) control has emerged as a prominent real-time network traffic signal control strategy due to its simplicity, decentralized structure, and theoretical guarantees of network queue stability. Meanwhile, advances in connected vehicle (CV) technology have sparked extensive research into CV-based traffic signal control. Despite these developments, few studies have investigated MP control in heterogeneously distributed and partially CV environments while ensuring network queue stability. To address these research gaps, we propose a CV-based MP control (CV-MP) method that leverages real-time CV travel time information to compute the pressure, thereby incorporating both the spatial distribution and temporal delays of vehicles, unlike existing approaches that utilized only spatial distribution or temporal delays. In particular, we establish sufficient conditions for road network queue stability that are compatible with most existing MP control methods. Moreover, we pioneered the proof of network queue stability even if the vehicles are only partially connected and heterogeneously distributed, and gave a necessary condition of CV observation for maintaining the stability. Evaluation results on an Amsterdam corridor show that CV-MP significantly reduces vehicle delays compared to both actuated control and conventional MP control across various CV penetration rates. Moreover, in scenarios with dynamic traffic demand, CV-MP achieves lower spillover peaks even with low and heterogeneous CV penetration rates, further highlighting its effectiveness and robustness.