Product understanding refers to a series of product-centric tasks, such as classification, alignment and attribute values prediction, which requires fine-grained fusion of various modalities of products. Excellent product modeling ability will enhance the user experience and benefit search and recommendation systems. In this paper, we propose MBSD, a pre-trained vision-and-language model which can integrate the heterogeneous information of product in a single stream BERT-style architecture. Compared with current approaches, MBSD uses a lightweight convolutional neural network instead of a heavy feature extractor for image encoding, which has lower latency. Besides, we cleverly utilize user behavior data to design a two-stage pre-training task to understand products from different perspectives. In addition, there is an underlying imbalanced problem in multimodal pre-training, which will impairs downstream tasks. To this end, we propose a novel self-distillation strategy to transfer the knowledge in dominated modality to weaker modality, so that each modality can be fully tapped during pre-training. Experimental results on several product understanding tasks demonstrate that the performance of MBSD outperforms the competitive baselines.