This research introduces a two-stage deep reinforcement learning approach for the cooperative path planning of unmanned surface vehicles (USVs). The method is designed to address cooperative collision-avoidance path planning while adhering to the International Regulations for Preventing Collisions at Sea (COLREGs) and considering the collision-avoidance problem within the USV fleet and between USVs and target ships (TSs). To achieve this, the study presents a dual COLREGs-compliant action-selection strategy to effectively manage the vessel-avoidance problem. Firstly, we construct a COLREGs-compliant action-evaluation network that utilizes a deep learning network trained on pre-recorded TS avoidance trajectories by USVs in compliance with COLREGs. Then, the COLREGs-compliant reward-function-based action-selection network is proposed by considering various TS encountering scenarios. Consequently, the results of the two networks are fused to select actions for cooperative path-planning processes. The path-planning model is established using the multi-agent proximal policy optimization (MAPPO) method. The action space, observation space, and reward function are tailored for the policy network. Additionally, a TS detection method is introduced to detect the motion intentions of TSs. The study conducted Monte Carlo simulations to demonstrate the strong performance of the planning method. Furthermore, experiments focusing on COLREGs-based TS avoidance were carried out to validate the feasibility of the approach. The proposed TS detection model exhibited robust performance within the defined task.