We consider continuous-time systems with input, output and additive disturbances in the particular case where the measurements are only available at discrete instants and have disturbances. To solve a state estimation problem, we construct continuous discrete interval observers that are asymptotically stable in the absence of disturbances. These interval observers are composed of two copies of the studied system and of a framer, accompanied with appropriate outputs which give, componentwise, upper and lower bounds for the solutions of the studied system. (C) 2014 Elsevier Ltd. All rights reserved.