A dialogue is essentially a multi-turn interaction among interlocutors. Effective evaluation metrics should reflect the dynamics of such interaction. Existing automatic metrics are focused very much on the turn-level quality, while ignoring such dynamics. To this end, we propose DynaEval, a unified automatic evaluation framework which is not only capable of performing turn-level evaluation, but also holistically considers the quality of the entire dialogue. In DynaEval, the graph convolutional network (GCN) is adopted to model a dialogue in totality, where the graph nodes denote each individual utterance and the edges represent the dependency between pairs of utterances. A contrastive loss is then applied to distinguish well-formed dialogues from carefully constructed negative samples. Experiments show that DynaEval significantly outperforms the state-of-the-art dialogue coherence model, and correlates strongly with human judgements across multiple dialogue evaluation aspects at both turn and dialogue level.