Our comprehension of stellar evolution on the AGB still faces many difficulties. To improve on this, a quantified understanding of large-amplitude pulsator atmospheres and interpretation in terms of their fundamental stellar parameters are essential. Aims. We wish to evaluate the effectiveness of the recently released CODEX dynamical model atmospheres in representing M-type Mira variables through a confrontation with the time-resolved spectro-photometric and interferometric PTI data set of TU And. Methods. We calibrated the interferometric K-band time series to high precision. This results in 50 nights of observations, covering 8 subsequent pulsation cycles. At each phase, the flux at 2.2 μm is obtained, along with the spectral shape and visibility points in 5 channels across the K-band. We compared the data set to the relevant dynamical, self-excited CODEX models. Results. Both spectrum and visibilities are consistently reproduced at visual minimum phases. Near maximum, our observations show that the current models predict a photosphere that is too compact and hot, and we find that the extended atmosphere lacks H2O opacity. Since coverage in model parameter space is currently poor, more models are needed to make firm conclusions on the cause of the discrepancies. We argue that for TU And, the discrepancy could be lifted by adopting a lower value of the mixing length parameter combined with an increase in the stellar mass and/or a decrease in metallicity, but this requires the release of an extended model grid.