Multiword expression (MWE) identification in tweets is a complex task due to the complex linguistic nature of MWEs combined with the non-standard language use in social networks. MWE features were shown to be helpful for hate speech detection (HSD). In this article, we present joint experiments on these two related tasks on English Twitter data: first we focus on the MWE identification task, and then we observe the influence of MWE-based features on the HSD task. For MWE identification, we compare the performance of two systems: lexicon-based and deep neural networks-based (DNN). We experimentally evaluate seven configurations of a state-of-the-art DNN system based on recurrent networks using pre-trained contextual embeddings from BERT. The DNN-based system outperforms the lexicon-based one thanks to its superior generalisation power, yielding much better recall. For the HSD task, we propose a new DNN architecture for incorporating MWE features. We confirm that MWE features are helpful for the HSD task. Moreover, the proposed DNN architecture beats previous MWE-based HSD systems by 0.4 to 1.1 F-measure points on average on four Twitter HSD corpora.