Clickbait is a form of web content designed to attract attention and entice users to click on specific hyperlinks. The detection of clickbaits is an important task for online platforms to improve the quality of web content and the satisfaction of users. Clickbait detection is typically formed as a binary classification task based on the title and body of a webpage, and existing methods are mainly based on the content of title and the relevance between title and body. However, these methods ignore the stylistic patterns of titles, which can provide important clues on identifying clickbaits. In addition, they do not consider the interactions between the contexts within title and body, which are very important for measuring their relevance for clickbait detection. In this paper, we propose a clickbait detection approach with style-aware title modeling and co-attention. Specifically, we use Transformers to learn content representations of title and body, and respectively compute two content-based clickbait scores for title and body based on their representations. In addition, we propose to use a character-level Transformer to learn a style-aware title representation by capturing the stylistic patterns of title, and we compute a title stylistic score based on this representation. Besides, we propose to use a co-attention network to model the relatedness between the contexts within title and body, and further enhance their representations by encoding the interaction information. We compute a title-body matching score based on the representations of title and body enhanced by their interactions. The final clickbait score is predicted by a weighted summation of the aforementioned four kinds of scores. Extensive experiments on two benchmark datasets show that our approach can effectively improve the performance of clickbait detection and consistently outperform many baseline methods.