Starting from the discrete-time affine term structure model by Dai, Le & Singleton (2006), this paper proposes a Radon-Nikodym derivative which implies that factors follow a mixture distribution under the physical measure. The model thus maintains attractive features of an affine relation between yields and factors, while allowing for nonlinear and non-normal time-series dynamics. Empirically the fit of the discrete-time 3-factor affine model is found to be substantially improved by the inclusion of two components to describe the time-series dynamics. Relative to the risk-neutral model, the mixture model is able to let the variance of the one-period rate be higher and faster increasing in the variance factor, and to introduce negative skewness and positive excess kurtosis. When weights on the components depend on factors, the model produces a speed of mean reversion and variance of the one-period rate that both increase fast with higher levels of the yield curve. The added second component is found to capture infrequent relatively large simultaneous shifts in direction of a yield curve that is at a lower level, is steeper, and is more positively curved.