Spectrum sharing is a pivotal technology for integrated satellite-maritime network to improve spectrum efficiency. However, the majority of existing spectrum sharing approaches relied on time-frequency multiplexing to circumvent or suppress interference, and often overlooked the problem of incomplete observability and interference present in heterogeneous systems. This limitation hindered overall system throughput improvements. In this article, an intelligent spectrum sharing strategy for integrated satellite-maritime heterogeneous mobile networks is firstly proposed. This strategy aims to operate co-frequency communication transmissions within the interference constraints, as derived from protocols and standards of International Telecommunication Union (ITU), to maximize the overall system throughput and spectral efficiency. Furthermore, considering the limitation that the satellite cannot fully observe channel statuses, we model the spectrum sharing process as a Partially Observable Markov Decision Process (POMDP). We employ an algorithm architecture that combines Dueling Deep Q-learning Network (DQN) and Double DQN to address this challenge, which enables satellites to efficiently evaluate the value of all channel allocation actions, thereby enhancing decision-making accuracy and algorithm convergence speed. Simulation results validate the superiority of our proposed strategy over compared methods in terms of throughput and stability.