We consider the problem of simultaneous reduction of acoustic echo, reverberation and noise. In real scenarios, these distortion sources may occur simultaneously and reducing them implies combining the corresponding distortion-specific filters. As these filters interact with each other, they must be jointly optimized. We propose to model the target and residual signals after linear echo cancellation and dereverberation using a multichannel Gaussian modeling framework and to jointly represent their spectra by means of a neural network. We develop an iterative block-coordinate ascent algorithm to update all the filters. We evaluate our system on real recordings of acoustic echo, reverberation and noise acquired with a smart speaker in various situations. The proposed approach outperforms in terms of overall distortion a cascade of the individual approaches and a joint reduction approach which does not rely on a spectral model of the target and residual signals.