This work deals with the combined effect of nonlinear distortions and inter-channel interference in millimeter wave multi-input multi-output (MIMO) communications. Deep neural networks (DNNs) can be used to handle the effect, but they often require a large number of pilot symbols, hindering their applications. With the aim of online training using a relatively small number of pilot symbols, we design a deep neural network (DNN) architecture carefully, which consists of a fully connected linear hidden layer and a non-fully connected nonlinear hidden layer. The linear hidden layer is used to deal with the co-channel interference and the nonlinear hidden layer is used to handle the nonlinear distortions. Moreover, the parameters of the DNN are properly tied to reduce the number of independent parameters. With such a DNN, the receiver is much efficient in terms of training overhead and symbol error rate performance, compared to conventional (DNN-based) techniques. Simulation results demonstrate the superiority of the proposed DNN-based receiver.