Sliding-mode observers are used to construct unknown input estimators. Then, these unknown input estimators are combined with sensor fault estimation schemes into one architecture that employs two sliding-mode observers for simultaneously estimating the plant's actuator faults (part of the unknown input) and detecting sensor faults. Closed form expressions are presented for the estimates of unknown inputs and sensor faults. A benchmark example of a controlled inverted pendulum system from the literature is utilized in the simulation study. The study shows that the observers analyzed in this paper generate good estimates of the unknown input and sensor faults signals in noisy environments for nonlinear plants.