Internet memes have become a powerful means for individuals to express emotions, thoughts, and perspectives on social media. While often considered as a source of humor and entertainment, memes can also disseminate hateful content targeting individuals or communities. Most existing research focuses on the negative aspects of memes in high-resource languages, overlooking the distinctive challenges associated with low-resource languages like Bengali (also known as Bangla). Furthermore, while previous work on Bengali memes has focused on detecting hateful memes, there has been no work on detecting their targeted entities. To bridge this gap and facilitate research in this arena, we introduce a novel multimodal dataset for Bengali, BHM (Bengali Hateful Memes). The dataset consists of 7,148 memes with Bengali as well as code-mixed captions, tailored for two tasks: (i) detecting hateful memes, and (ii) detecting the social entities they target (i.e., Individual, Organization, Community, and Society). To solve these tasks, we propose DORA (Dual cO-attention fRAmework), a multimodal deep neural network that systematically extracts the significant modality features from the memes and jointly evaluates them with the modality-specific features to understand the context better. Our experiments show that DORA is generalizable on other low-resource hateful meme datasets and outperforms several state-of-the-art rivaling baselines.