Electroencephalography (EEG)-based emotion classification during music listening has gained increasing attention nowadays due to its promise of potential applications such as musical affective brain-computer interface (ABCI), neuromarketing, music therapy, and implicit multimedia tagging and triggering. However, music is an ecologically valid and complex stimulus that conveys certain emotions to listeners through compositions of musical elements. Using solely EEG signals to distinguish emotions remained challenging. This study aimed to assess the applicability of a multimodal approach by leveraging the EEG dynamics and acoustic characteristics of musical contents for the classification of emotional valence and arousal. To this end, this study adopted machine-learning methods to systematically elucidate the roles of the EEG and music modalities in the emotion modeling. The empirical results suggested that when whole-head EEG signals were available, the inclusion of musical contents did not improve the classification performance. The obtained performance of 74~76% using solely EEG modality was statistically comparable to that using the multimodality approach. However, if EEG dynamics were only available from a small set of electrodes (likely the case in real-life applications), the music modality would play a complementary role and augment the EEG results from around 61-67% in valence classification and from around 58-67% in arousal classification. The musical timber appeared to replace less-discriminative EEG features and led to improvements in both valence and arousal classification, whereas musical loudness was contributed specifically to the arousal classification. The present study not only provided principles for constructing an EEG-based multimodal approach, but also revealed the fundamental insights into the interplay of the brain activity and musical contents in emotion modeling.