Domain mismatch is a noteworthy issue in acoustic event detection tasks, as the target domain data is difficult to access in most real applications. In this study, we propose a novel CNN-based discriminative training framework as a domain compensation method to handle this issue. It uses a parallel CNN-based discriminator to learn a pair of high-level intermediate acoustic representations. Together with a binary discriminative loss, the discriminators are forced to maximally exploit the discrimination of heterogeneous acoustic information in each audio clip with target events, which results in a robust paired representations that can well discriminate the target events and background/domain variations separately. Moreover, to better learn the transient characteristics of target events, a frame-wise classifier is designed to perform the final classification. In addition, a two-stage training with the CNN-based discriminator initialization is further proposed to enhance the system training. All experiments are performed on the DCASE 2018 Task3 datasets. Results show that our proposal significantly outperforms the official baseline on cross-domain conditions in AUC by relative $1.8-12.1$% without any performance degradation on in-domain evaluation conditions.