Context. Modeling stellar atmospheres is a complex and intriguing task in modern astronomy. A systematic comparison of models with multi-technique observations is the only efficient way to constrain the models. Aims. We intend to perform self-consistent modeling of the atmospheres of six carbon-rich AGB stars (R Lep, R Vol, Y Pav, AQ Sgr, U Hya, and X TrA) with the aim of enlarging the knowledge of the dynamic processes occurring in their atmospheres. Methods. We used VLTI/MIDI interferometric observations, in combination with spectro-photometric data, and compared them with self-consistent, dynamic model atmospheres. Results. We found that the models can reproduce spectral energy distribution (SED) data well at wavelengths longer than 1 µm, and the interferometric observations between 8 µm and 10 µm. Discrepancies observed at wavelengths shorter than 1 µm in the SED, and longer than 10 µm in the visibilities, could be due to a combination of data-and model-related effects. The models best fitting the Miras are significantly extended, and have a prominent shell-like structure. On the contrary, the models best fitting the non-Miras are more compact, showing lower average mass loss. The mass loss is of episodic or multi-periodic nature but causes the visual amplitudes to be notably larger than the observed ones. A number of stellar parameters were derived from the model fitting: T Ross , L Ross , M, C/O, andṀ. Our findings agree well with literature values within the uncertainties. T Ross , and L Ross are also in good agreement with the temperature derived from the angular diameter T (θ (V−K) ) and the bolometric luminosity from the SED fitting L bol , except for AQ Sgr. The possible reasons are discussed in the text. Finally, θ Ross and θ (V−K) agree with one another better for the Miras than for the nonMiras targets, which is probably connected to the episodic nature of the latter models. We also located the stars in the H-R diagram, comparing them with evolutionary tracks. We found that the main derived properties (L, T eff , C/O ratios and stellar masses) from the model fitting are in good agreement with TP-AGB evolutionary calculations for carbon stars carried out with the COLIBRI code.