Underwater acoustic sensor networks (UASNs) are widely used in a variety of ocean applications, such as exploring ocean resources or monitoring abnormal ocean environments. However, data collection schemes in UASNs are significantly different from those in wireless sensor networks due to high power consumption, severe propagation delay, and so on. Furthermore, previous research has overlooked practical conditions, such as characteristics of water delamination and energy constraint on autonomous underwater vehicles (AUVs). In this paper, a stratification-based data collection scheme for three-dimensional UASNs is proposed to solve these problems. In this scheme, the network is divided into two layers on the basis of the Ekman drift current model. The upper layer, called the Ekman layer, suffers large water velocity. Thus, nodes in the upper layer will follow the water flow. In this case, we employ a forward set-based multihop forwarding algorithm for data collection. The lower layer suffers small water velocity so that nodes in this layer are considered as relatively static. A neighbor density clustering-based AUV data gathering algorithm is applied in this layer for data collection. By employing different data collection algorithms in different layers, we can integrate the advantages of a multihop transmission scheme and AUV-aided data collection scheme to reduce network consumption and improve network lifetime. The simulation results also confirm the proposed method has good performance.