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We propose an independence-based joint dereverberation and separation method with a neural source model. We introduce a neural network in the framework of time-decorrelation iterative source steering, which is an extension of independent vector analysis to joint dereverberation and separation. The network is trained in an end-to-end manner with a permutation invariant loss on the time-domain separation output signals. Our proposed method can be applied in any situation with at least as many microphones as sources, regardless of their number. In experiments, we demonstrate that our method results in high performance in terms of both speech quality metrics and word error rate (WER), even for mixtures with a different number of speakers than training. Furthermore, the model, trained on synthetic mixtures, without any modifications, greatly reduces the WER on the recorded dataset LibriCSS.