This paper provides evidence that interbank markets are tiered rather than flat, in the sense that most banks do not lend to each other directly but through money center banks acting as intermediaries. We capture the concept of tiering by developing a core-periphery model, and devise a procedure for fitting the model to real-world networks. Using Bundesbank data on bilateral interbank exposures among 2000 banks from 1999 to 2012, we find strong evidence of tiering in the German banking system. This extent of tiering is unlikely to arise in standard random networks. Indeed, we show that bank specialization and balance sheet variables predict how banks position themselves in the interbank market. This link provides a promising avenue for understanding the formation of financial networks.