The prevalence of memes in social media communication underscores their role in information dissemination. However, the potential for memes to spread negativity through offensive or harmful content is a significant concern. This negativity poses a challenge for sentiment analysis, mainly due to the multimodal nature of memes. To address this issue, this paper presents an intelligent multimodal framework (named M-SAM) for classifying Bengali memes into three sentiment categories: positive, negative, and neutral. Moreover, this work introduces new a corpus (M-SAD), encompassing 8361 memes. The proposed framework integrates visual and textual models, leveraging deep learning (DL) and transformer-based architectures. This work explored various DL (CNN, BiLSTM) and transformer-based models (Bangla-Bert-Base, m-BERT, XLM-R, BanglaBERT, and Indic-DistilBERT) to assess their efficacy in extracting textual features. Additionally, pre-trained visual models such as VGG16, VGG19, and ResNet50 were employed for extracting visual features. Furthermore, we investigated the late fusion method to integrate textual and visual features for multimodal training. The experimental results demonstrate that the proposed multimodal model (m-BERT + VGG16), leveraging m-BERT for textual features and VGG16 for visual features, achieves the highest weighted \(f_1\) -score of 0.749 among all multimodal methods, indicating its effectiveness in sentiment classification of Bengali memes.