Abstract: Dialogue representation and understanding aim to convert conversational inputs into embeddings and fulfill discriminative tasks. Compared with free-form text, dialogue has two important characteristics, hierarchical semantic structure and multi-facet attributes. Therefore, directly applying the pretrained language models (PLMs) might result in unsatisfactory performance. Recently, several work focused on the dialogue-adaptive post-training (DialPost) that further trains PLMs to fit dialogues. To model dialogues more comprehensively, we propose a DialPost method, Dialog-Post, with multi-level self-supervised objectives and a hierarchical model. These objectives leverage dialogue-specific attributes and use self-supervised signals to fully facilitate the representation and understanding of dialogues. The novel model is a hierarchical segment-wise self-attention network, which contains inner-segment and inter-segment self-attention sub-layers followed by an aggregation and updating module. To evaluate the effectiveness of our methods, we first apply two public datasets for the verification of representation ability. Then we conduct experiments on a newly-labelled dataset that is annotated with 4 dialogue understanding tasks. Experimental results show that our method outperforms existing SOTA models and achieves a 3.3\% improvement on average.