In this paper, we investigate the secure content delivery issue for device-to-device networks based on the trust evaluation mechanism and covert communication model. Specifically, in order to stimulate the lasting and rational cooperation among mobile devices, we propose a trust evaluation mechanism, where the trust degree between two mobile devices can be obtained through historical assessed values. Simultaneously, a covert communication model is introduced to guarantee the undetectability of content delivery, which helps to stop malicious wardens adopting some coming external attacks. In this way, the availability and dependability of content sharing, as well the confidentiality and integrity of transmitted contents cam be guaranteed. Then, combining security-aware metrics, in terms of trust degree and covert rate, with physical layer transmission performances, in terms of achievable rate and successful delivery probability, we propose the definition of secrecy-aware effective rate to serve as a guidance on the joint optimization issue of content delivery mode selection and resource management, which is formulated as a social welfare maximization problem. To solve the complex problem tactfully, it is decoupled into two subproblems, i.e., mode selection which is a many-to-one matching problem, and resource management which is a one-to-one matching problem. By analyzing the interaction between two issues, a novel hierarchical stable matching algorithm is proposed to obtain three-dimension stable matching results. Its properties, such as stability, convergence, optimality, and complexity, are theoretically analyzed and proved. Finally, extensive numerical results are provided to demonstrate the advantages of our proposed algorithms.