This paper deals with a multichannel audio source separation problem under underdetermined conditions. Multichannel non-negative matrix factorization (MNMF) is a powerful method for underdetermined audio source separation, which adopts the NMF concept to model and estimate the power spectrograms of the sound sources in a mixture signal. This concept is also used in independent low-rank matrix analysis (ILRMA), a special class of the MNMF 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 expressing source power spectrograms. This approach has performed impressively in determined source separation tasks thanks to the representation power of deep neural networks. While the original MVAE method was formulated under determined mixing conditions, this paper proposes a generalized version of it by combining the ideas of MNMF and MVAE so that it can also deal with underdetermined cases. We call this method the generalized MVAE (GMVAE) method. In underdetermined source separation and speech enhancement experiments, the proposed method performed better than baseline methods.