The development of advanced composite load models is imperative for accurate dynamic stability analysis of electric power systems. In North America, the Load Modelling Task Force (LMTF) endorsed the WECC composite load model for dynamic simulations of transmission networks. However, due to its complex dynamics and large number of parameters, little attention has been paid to the estimation of its parameters from online measurements. This load model incorporates the switching action of different built-in protection devices, which negatively affects the performance of conventional nonlinear programming algorithms. This paper introduces a hybrid optimization approach to estimate the parameters of the WECC composite load model. Parameters associated with dynamic and static equations, which are constrained by the physical interpretation of the model, are estimated by nonlinear programming techniques. On the other hand, protection parameters are estimated using a surrogate model of the objective function based on Radial Basis Function (RBF) optimization. The proposed scheme is validated with simulated and actual measurements collected across Australia.