Security analysis of composite protocols is a critical issue in the field of network security. In complex network environments, the traditional approach of analyzing a single protocol becomes inadequate when dealing with scenarios involving multiple interactions and combinations of protocols. To address this challenge, this paper extends the Logic of Events Theory (LoET) and proposes a method for proving the security of composite protocols. Building upon the Logic of Events Theory, we introduce sequential composition rules, ordering rules, and relevant axioms. We incorporate the concept of invariants and formally abstract the DTLS-SRTP protocol, thereby verifying the mutual authentication and confidentiality of the two sub-protocols. In conclusion, our study demonstrates that the extended Logic of Events Theory offers an effective means of verifying the security of composite protocols.