Semantically matching two text sequences (usually two sentences) is a fundamental problem in NLP. Most previous methods either encode each of the two sentences into a vector representation (sentence-level embedding) or leverage word-level interaction features between the two sentences. In this study, we propose to take the sentence-level embedding features and the word-level interaction features as two distinct views of a sentence pair, and unify them with a framework of Variational Autoencoders such that the sentence pair is matched in a semi-supervised manner. The proposed model is referred to as Dual-View Variational AutoEncoder (DV-VAE), where the optimization of the variational lower bound can be interpreted as an implicit Co-Training mechanism for two matching models over distinct views. Experiments on SNLI, Quora and a Community Question Answering dataset demonstrate the superiority of our DV-VAE over several strong semi-supervised and supervised text matching models.