A formulation is presented for modeling neutral atmosphere structure in an intermediate height region (70-130 km) between given lower and upper models in temperature, pressure, density and constituent gas concentrations and to maintain continuity in the second derivative of temperature and the other properties with respect to height. The method employs temperature as the prime parameter requiring simultaneously a best fit to available temperature data at the intermediate heights and hydrostatic consistency between the nitrogen partial pressures at 70 and 130 km. The method is well suited to upper and lower models that have analytical representations and is developed as the upper model and for polynomially-generated height-latitude cross-sections in the lower region. Attention is given to comparisons between observed and model temperatures and it is found that mid-latitude data (primarily obtained using the incoherent scatter technique) are on average higher than the models due to the requirement to maintain hydrostatic consistency in nitrogen partial pressures between the 70 km and 130 km values of the given lower and upper models. This discrepancy which at present remains an unresolved problem is discussed in the text. Tables of temperature, pressure, and density are included in the report based on the best fit to available data and simultaneously satisfying the constraints of the upper and lower models. Keywords: Temperature; Mesosphere; Pressure; Lower thermosphere; Density; Model atmospheres. (JHD).