In this paper we provide two methods that improve the detection of sound events in domestic environments. First, motivated by the broad categorization of domestic sounds as foreground or background events according to their spectro-temporal structure, we propose to learn a foreground-background classifier jointly with the sound event classifier in a multi-task fashion to improve the generalization of the latter. Second, while the semi-supervised learning capability adopted for training sound event detection systems with synthetic labeled data and unlabeled or partially labeled real data aims to learn invariant representations for both domains, there is still a gap in performance when testing such systems on real environments. To further reduce this data mismatch, we propose a domain adaptation strategy that aligns the empirical distributions of the feature representations of active and inactive frames of synthetic and real recordings via optimal transport. We show that these two approaches lead to enhanced detection performance in terms of the event-based macro F1-score on the DESED dataset.