Deep learning based speech enhancement and source separation systems have recently reached unprecedented levels of quality, to the point that performance is reaching a new ceiling. Most systems rely on estimating the magnitude of a target source by estimating a real-valued mask to be applied to a time-frequency representation of the mixture signal. A limiting factor in such approaches is a lack of phase estimation: the phase of the mixture is most often used when reconstructing the estimated time-domain signal. Here, we propose "magbook", "phasebook", and "combook", three new types of layers based on discrete representations that can be used to estimate complex time-frequency masks. Magbook layers extend classical sigmoidal units and a recently introduced convex softmax activation for mask-based magnitude estimation. Phasebook layers use a similar structure to give an estimate of the phase mask without suffering from phase wrapping issues. Combook layers are an alternative to the magbook-phasebook combination that directly estimate complex masks. We present various training and inference schemes involving these representations, and explain in particular how to include them in an end-to-end learning framework. We also present an oracle study to assess upper bounds on performance for various types of masks using discrete phase representations. We evaluate the proposed methods on the wsj0-2mix dataset, a well-studied corpus for single-channel speaker-independent speaker separation, matching the performance of state-of-the-art mask-based approaches without requiring additional phase reconstruction steps.