This paper deals with a multichannel audio source separation problem under underdetermined conditions. Multichannel Non-negative Matrix Factorization (MNMF) is one of powerful approaches, which adopts the NMF concept for source power spectrogram modeling. This concept is also employed in Independent Low-Rank Matrix Analysis (ILRMA), a special class of the MNMF framework formulated under determined conditions. While these methods work reasonably well for particular types of sound sources, one limitation is that they can fail to work for sources with spectrograms that do not comply with the NMF model. To address this limitation, an extension of ILRMA called the Multichannel Variational Autoencoder (MVAE) method was recently proposed, where a Conditional VAE (CVAE) is used instead of the NMF model for source power spectrogram modeling. This approach has shown to perform impressively in determined source separation tasks thanks to the representation power of DNNs. While the original MVAE method was formulated under determined mixing conditions, this paper generalizes it so that it can also deal with underdetermined cases. We call the proposed framework the Generalized MVAE (GMVAE). The proposed method was evaluated on a underdetermined source separation task of separating out three sources from two microphone inputs. Experimental results revealed that the GMVAE method achieved better performance than the MNMF method.