Model disturbances result from model uncertainties or external factors acting on the system. They usually affect the closed-loop performance in a control loop system. However, they are often unknown and cannot be then compensated. Therefore, it is crucial to develop estimation methods for the effective estimation of the disturbances which can be then considered appropriately in the control design. This paper proposes a hybrid method for the joint estimation of the state and the disturbance for a class of nonlinear systems in two steps. The approach consists in a neural network with time-varying weights used to approximate the disturbance term and a modulating function method for the finite-time estimation of the state and the weights. The modulating functions approach simplifies the estimation problem into solving an algebraic systems of equations. Both offline and online frameworks are presented and discussed. An example is presented to demonstrate the performance of the proposed algorithm.