When a nonstationary signal containing sudden changes, such as an image signal, is degraded by an additive noise, a powerful means to recover the signal is to use a nonlinear filter. This paper uses a layered neural network, and proposes a new method to construct a nonlinear filter for restoring a signal corrupted by mixed noise (i.e., mixed noise composed of Gaussian noise and impulse noise). As the first step, a prototype filter is proposed, which is a combination of a median filter and a linear (averaging) filter. Then, it is shown that the prototype filter can be represented by a network structure. By interpreting the network representation by a layered neural network, the idea is extended to the median neural network hybrid (MNNH) filter. The MNNH filter can be trained by the back-propagation algorithm. The prototype filter already has a high mixed noise elimination performance, but the MNNH filter can further improve the performance by reflecting information on the signal to be processed (the original image and the additive noise) when such information is given. Lastly, the usefulness of the MNNH filter is demonstrated through various application examples.