Automatic dialogue coherence evaluation has attracted increasing attention and is crucial for developing promising dialogue systems. However, existing metrics have two major limitations: (a) they are mostly trained in a simplified two-level setting (coherent vs. incoherent), while humans give Likert-type multi-level coherence scores, dubbed as “quantifiable”; (b) their predicted coherence scores cannot align with the actual human rating standards due to the absence of human guidance during training. To address these limitations, we propose Quantifiable Dialogue Coherence Evaluation (QuantiDCE), a novel framework aiming to train a quantifiable dialogue coherence metric that can reflect the actual human rating standards. Specifically, QuantiDCE includes two training stages, Multi-Level Ranking (MLR) pre-training and Knowledge Distillation (KD) fine-tuning. During MLR pre-training, a new MLR loss is proposed for enabling the model to learn the coarse judgement of coherence degrees. Then, during KD fine-tuning, the pretrained model is further finetuned to learn the actual human rating standards with only very few human-annotated data. To advocate the generalizability even with limited fine-tuning data, a novel KD regularization is introduced to retain the knowledge learned at the pre-training stage. Experimental results show that the model trained by QuantiDCE presents stronger correlations with human judgements than the other state-of-the-art metrics.