To handle the state estimation of a nonlinear system perturbed by a scalar disturbance distributed by a known nonlinear vector, a sliding-mode term is incorporated into the nonlinear high-gain observer (HGO) to realize a robust HGO. By imposing a structural assumption on the unknown input distribution vector, the observability of the disturbance with respect to the output is safeguarded, and the disturbance can be estimated from the sliding surface. Under a Lipschitz condition for the nonlinear part, the nonlinear observers are designed under the structural assumption that the system is observable with respect to any input. In the sliding mode, the disturbance under an equivalent control becomes an increment of Lipschitzian function, and the convergence of the estimation error dynamics can be proven similar to the analysis of HGOs. The proposed technique can be applied for fault detection and isolation. The simulation results for the bioreactor application demonstrate the effectiveness of the proposed method.