The International Classification of Diseases (ICD) is the foundation of global health statistics and epidemiology. The ICD is designed to translate health conditions into alphanumeric codes. A number of approaches have been proposed for automatic ICD coding, since manual coding is labor-intensive and there is a global shortage of healthcare workers. However, existing studies did not exploit the discourse structure of clinical notes, which provides rich contextual information for code assignment. In this paper, we exploit the discourse structure by leveraging section type classification and section type embeddings. We also focus on the class-imbalanced problem and the heterogeneous writing style between clinical notes and ICD code definitions. The proposed reconciled embedding approach is able to tackle them simultaneously. Experimental results on the MIMIC dataset show that our model outperforms all previous state-of-the-art models by a large margin. The source code is available at https://github.com/discnet2022/discnet