We present a unifying framework for dealing with convolutive blind source separation (BSS), which fully models inter-channel, inter-frequency, and inter-frame correlation of sources by latent covariance matrices subject to a joint diagonalizability constraint. The framework is shown to encompass as its specific realizations a variety of standard BSS and dereverberation methods that have been developed independently, including frequency-domain independent component analysis (FDICA), fast full-rank spatial covariance analysis (FastFCA), and weighted prediction error (WPE). This gives a unified view of conventional methods and a systematic way of deriving new BSS methods. A BSS experiment on speech mixtures showed improved separation performance of a proposed method compared to the state-of-the-art independent low-rank matrix analysis.