Unmanned aerial vehicles (UAVs) have numerous applications in reconnaissance, search, and rescue missions. However, searching underwater areas remains a challenge for UAVs. For anti-submarine search tasks, this paper proposes using a mixed swarm of UAVs and unmanned surface vehicles (USVs). To generate vehicle paths with the goal of minimizing the travel time while achieving complete coverage, a two-phase strategy is developed. In the first phase, optimal waypoints are determined to balance the task volume among the UAVs and USVs. A mapping model is constructed to represent the relationships between the different unmanned platforms and the mission environment. In the second phase, the search trajectory for each UAV/USV is generated by combining waypoint clustering and closed-loop trajectory generation. A detailed simulation study confirms the feasibility and flexibility of the proposed path planning method when applied to cross-domain swarms of different types and sizes for anti-submarine missions. In addition, the simulation results show that cross-domain cooperative planning for unmanned platforms may have advantages over single-domain planning in some scenarios.