For a family of nonlinear discrete-time systems with input, output and uncertain terms, a new interval observer is designed. Its main feature is that it is composed of two copies of classical observers. This interval observer applies in the presence of unknown bounded nonlinear terms and additive disturbances and is used to achieve asymptotic stability through an appropriate choice of dynamic output feedback. An illustrative example completes the presentation. (C) 2013 Elsevier Ltd. All rights reserved.