Protein-protein interactions (PPIs) are essential for many biological processes, but their design is challenging due to their complex and dynamic nature. We propose a new model called Hierarchical Interface CO-design Network (HICON) that can jointly generate the sequence and 3D structure of protein interfaces. HICON uses a novel hierarchical architecture that combines atomic and amino acid resolutions in an equivariant manner and leverages Large Protein Language Models for sequence initialization. We evaluate HICON on a variety of biological interfaces, including protein-protein, enzyme-ligand, and antibody paratope-epitope interfaces. Our results show that HICON outperforms state-of-the-art models on sequence prediction and paratope co-design on several computational metrics.