Integrated Internet MANET (IIM) is a heterogeneous network which is shaped by the interconnection of the wired internet and the wireless mobile ad hoc network. It allows uninhibitedly moving nodes in MANETs to interact with the fixed nodes in internet through the gateway. IIM experiences many security issues due to open wireless medium and lack of mutual authentication between nodes. The existing method provides the security management by data integrity and confidentiality. However, Major disadvantage of symmetric key cryptography is key distribution in network. In MANETs due to mobility and constraint resources key distribution is very much challenging task. Mutual authenticated key agreement technique securely agree on session key between communicating entities, & is also used for secure communication and protection of data from malicious activities. In order to provide mutual authentication between mobile node and a fixed node in IIM, two problems must be overcome i.e. key management and computational cost. Strength of any security algorithm relies on its key management technique with minimum overhead as IIM is resource constraint network. We propose a method to provide mutual authentication between communicating entities using chaos theory. It overcomes the key management cost by avoiding modular exponentiation and scalar multiplications. Moreover our proposed method mutually authenticated key agreement protocol provides a mechanism to securely agree the session key between source and destination. Through extensive simulation analysis, we conclude that the proposed method provides a better approach towards security and protection of data from malicious nodes with minimum overhead in IIM.