DNA-Encoded Library (DEL) has proven to be a powerful tool that utilizes combinatorially constructed small molecules to facilitate highly-efficient screening assays. These selection experiments, involving multiple stages of washing, elution, and identification of potent binders via unique DNA barcodes, often generate complex data. This complexity can potentially mask the underlying signals, necessitating the application of computational tools such as machine learning to uncover valuable insights. We introduce a compositional deep probabilistic model of DEL data, DEL-Compose, which decomposes molecular representations into their mono-synthon, di-synthon, and tri-synthon building blocks and capitalizes on the inherent hierarchical structure of these molecules by modeling latent reactions between embedded synthons. Additionally, we investigate methods to improve the observation models for DEL count data such as integrating covariate factors to more effectively account for data noise. Across two popular public benchmark datasets (CA-IX and HRP), our model demonstrates strong performance compared to count baselines, enriches the correct pharmacophores, and offers valuable insights via its intrinsic interpretable structure, thereby providing a robust tool for the analysis of DEL data.