The advances in AI-enabled techniques have accelerated the creation and automation of visualizations in the past decade. However, presenting visualizations in a descriptive and generative format remains a challenge. Moreover, current visualization embedding methods focus on standalone visualizations, neglecting the importance of contextual information for multi-view visualizations. To address this issue, we propose a new representation model, Chart2Vec, to learn a universal embedding of visualizations with context-aware information. Chart2Vec aims to support a wide range of downstream visualization tasks such as recommendation and storytelling. Our model considers both structural and semantic information of visualizations in declarative specifications. To enhance the context-aware capability, Chart2Vec employs multi-task learning on both supervised and unsupervised tasks concerning the cooccurrence of visualizations. We evaluate our method through an ablation study, a user study, and a quantitative comparison. The results verified the consistency of our embedding method with human cognition and showed its advantages over existing methods.