We have observed Mira stars with the FLUOR beamcombiner on the IOTA interferometer in narrow bands around 2.2 mum wavelength. We find systematically larger diameters in bands contaminated by water vapor and CO. The visibility measurements can be interpreted with a model comprising a photosphere surrounded by a thin spherical molecular layer. The high quality of the fits we obtain demonstrates that this simple model accounts for most of the star's spatial structure. For each star and each period we were able to derive the radius and temperature of the star and of the molecular layer as well as the optical depth of the layer in absorption and continuum bands. The typical radius of the molecular layer is 2.2 R-star with a temperature ranging between 1500 and 2100 K. The photospheric temperatures we find are in agreement with spectral types of Mira stars. Our photospheric diameters are found smaller than in previous studies by several tens of percent. We believe previous diameters were biased by the use of unsuited geometrical models to explain visibilities. The conclusions of this work are various. First, we offer a consistent view of Mira stars over a wide range of wavelengths. Second, the parameters of the molecular layer we find are consistent with spectroscopic studies. Third, from our diameter measurements we deduce that all Mira stars are fundamental mode pulsators and that previous studies leading to the conclusion of the first-overtone mode were biased by too large diameter estimates.