Two refined structural model proposed for the thermo-elastic behavior of the rib-reinforced composite medium with the total anisotropy of the material components of the composition. As criteria of equivalence of the rib-reinforced compositions to fictitious homogeneous anisotropic material the equality of specific free energy and specific thermodynamic Gibbs energy in them are used. This allows determining upper and lower bounds of the effective stiffness of the composite material. Verification of the model is carried out by comparing the effective elastic constants of the foam plastic medium reinforced in the form of honeycomb cell with the results of the standard calculations performed on the basis of the finite-element modeling and also by comparing similar values for lightweight honeycomb filler with the results of the experiment. It was shown that refined lower bounds of effective rigidities better agreed with the experimental data and with reference calculations than the calculated values of the same values that are defined on the basis of other structural models.