Distribution mismatches between the data seen at training and at application time remain a major challenge in all application areas of machine learning. We study this problem in the context of machine listening (Task 1b of the DCASE 2019 Challenge). We propose a novel approach to learn domain-invariant classifiers in an end-to-end fashion by enforcing equal hidden layer representations for domain-parallel samples, i.e. time-aligned recordings from different recording devices. No classification labels are needed for our domain adaptation (DA) method, which makes the data collection process cheaper.