This paper addresses the problem of composite inverse optimal control for a class of uncertain nonlinear systems affected by unmatched disturbances. A control framework is proposed by integrating a generalized proportional integral observer (GPIO) with a neural network based scheme to simultaneously estimate both matched and mismatched disturbances and to approximate unknown system nonlinearities. To overcome the computational challenges associated with solving the nonlinear Hamilton-Jacobi-Bellman (HJB) equation in high-order systems, a composite adaptive inverse optimal control (IOC) strategy is developed. This approach combines GPIOs with the IOC framework, effectively utilizing the available system information while providing adaptive capability in dynamically changing environments. A rigorous theoretical analysis is presented to guarantee both stability and optimality of closed-loop system. The effectiveness and robustness of the proposed method are demonstrated through simulation studies.