Many audio signal processing algorithms rely on the estimation of magnitude or complex short-time Fourier transform (STFT) spectrograms, but usually do not take into account the necessity for the estimated spectrograms to be consistent, i.e., to correspond to the STFT of a real-valued time-domain signal. Consistency constraints were introduced in [1] and applied there to phase reconstruction from magnitude spectrograms. In this paper, we show how to use them to introduce penalty functions on the consistency of STFT spectrograms into the recently introduced complex non-negative matrix factorization (NMF) framework [2], which estimates recurring patterns in the observed magnitude spectra, their activations and their phases. We derive analytical update equations through an auxiliary function approach, and present preliminary results on a supervised monaural source separation task.