We study a decision maker who approaches an uncertain decision problem by formulating a set of plausible probabilistic models of the environment but is aware that these models are only stylized and incomplete approximations. The agent is effectively facing two layers of uncertainty. Not only is the decision maker uncertain regarding what model in this set has the best fit (model ambiguity), but she is also concerned that the best-fit model itself might be a poor description of the environment (model misspecification). We develop an axiomatic foundation for a general class of preferences that capture concern toward these two layers of uncertainty and allow us to compare individuals’ degrees of aversion to model misspecification and model ambiguity independently of each other.