We propose a no-arbitrage model that jointly explains the dynamics of consumer prices as well as the nominal and real term structures of risk-free rates. In our framework, distinct core, food, and energy price series combine into a measure of total inflation to price nominal Treasuries. This approach captures different frequencies in inflation fluctuations: Shocks to core are more persistent and less volatile than shocks to food and, especially, energy (the 'crust'). We find that a common structure of latent factors determines and predicts the term structure of yields and inflation. The model outperforms popular benchmarks and is at par with the Survey of Professional Forecasters in forecasting inflation. Real rates implied by our model uncover the presence of a time-varying component in TIPS yields that we attribute to disruptions in the inflation-indexed bond market. Finally, we find a pronounced declining pattern in the inflation risk premium that illustrates the changing nature of inflation risk in nominal Treasuries.