Unmanned Aerial Vehicle (UAV) has been widely adopted in logistics systems with improved flexibility, efficiency, and lowered cost. However, limited by capacity and endurance, UAVs often need to cooperate with ground vehicles or humans. This work considers a practical medical delivery problem in which multiple pharmacies share a fleet of vehicles to provide urgent medical delivery services to hospitals. To further improve its operational efficiency while reducing cost, a novel delivery mode is proposed, in which human couriers and UAVs collaboratively fulfill the medical delivery tasks. Considering the heterogeneity of the fleets, the time-sensitive nature of urgent orders, and constraints like vehicle capacities, this problem is modeled as the Multi-depot Pickup and Delivery Problem with Soft Deadlines (MPDPSD), and a heuristic-based method is proposed. Through extensive computational experiments, it is proved that the proposed method can provide feasible solutions with good performance for practical medical delivery service in a short time. In addition, the collaboration mode performs better than conventional human-only mode.