Future generation communication systems are exemplified by 5G and 6G wireless technologies, and the utilization of integrated air-to-sea (A2S) communication infrastructure is employed to extend network coverage and enhance data throughput to support data-driven maritime applications. These ground-breaking techniques have promoted the rapid development of the maritime internet of things (MIoT). In particular, the integration of air base stations (ABSs) in the MIoT can achieve broadband, low-delay, and reliable wireless transmissions. Considering the potential of ABS-enabled communications, this survey presents the state of the art in the A2S integrated MIoT. More specifically, relevant A2S integrated MIoT architectures are discussed together with the role of their building blocks. Next, we introduce the enabling technologies, including the sensor, communication, data processing and storage, and security and privacy protection techniques. Then, resource allocation, cloud/edge computing and caching, routing protocols, and spatial location optimization in the maritime environment are discussed and grouped based on their performance targets. Additionally, we also show the potential applications of the A2S integrated MIoT in marine environment monitoring, traffic, navigation safety, and resources management. Finally, several future challenges in the area of the A2S integrated MIoT are given, related to the technical security, reliability, and energy efficiency, etc.