Machine learning has been successfully applied to various fields in computational science and engineering. In this paper, we propose interfaced neural networks (INNs) to solve interface problems with discontinuous coefficients as well as irregular interfaces. Unlike using a single network, which has been found to be almost unable to retain the inherent properties of interface problems, INN decomposes the computational domain into several subdomains according to the interface and leverages multiple networks, each of which is responsible for the solution on one subdomain. An extended multiple-gradient descent (MGD) method is introduced during the training phase, which utilizes multiple-gradient information to adaptively balance the interplay between different terms in the loss function. The effectiveness, accuracy and robustness of the proposed framework are demonstrated through a collection of interface problems in two and three spatial dimensions, including a moving interface case.