Biophysically realistic models of the cochlea are based on cascaded transmission-line (TL) models which capture longitudinal coupling, cochlear nonlinearities, as well as the human frequency selectivity. However, these models are slow to compute (order of seconds/minutes) while machine-hearing and hearing-aid applications require a real-time solution. Consequently, real-time applications often adopt more basic and less time-consuming descriptions of cochlear processing (gamma-tone, dual resonance nonlinear) even though there are clear advantages in using more biophysically correct models. To overcome this, we recently combined nonlinear Deep Neural Networks (DNN) with analytical TL cochlear model descriptions to build a real-time model of cochlear processing which captures the biophysical properties associated with the TL model. In this work, we aim to extend the normal-hearing DNN-based cochlear model (CoNNear) to simulate frequency-specific patterns of hearing sensitivity loss, yielding a set of normal and hearing-impaired auditory models which can be computed in real-time and are differentiable. They can hence be used in backpropagation networks to develop the next generation of hearing-aid and machine hearing applications.