The article is concerned with the prediction of effective thermoelastic properties of balanced plain weave textile fabrics bonded to a polysiloxane matrix. While actual applications assume ceramic matrices, we limit our attention to their polymeric precursors and concentrate on computational aspects of both analytical and numerical homogenization. Two types of reinforcements, basalt and carbon, are considered to study the influence of microstructural details on the estimates of overall properties. Attention is focused on the previously developed numerical approach effectively combining the Mori-Tanaka micromechanical model, two-layer statistically equivalent periodic unit cell analyzed with the help of the extended finite element method (XFEM), and information about microstructure configuration provided by standard image processing as well as X-ray microtomography. The main goal is to validate this approach by comparing the numerically obtained data with those obtained experimentally by exploiting the nondestructive measurements of ultrasonic wave speed. Moreover, a pure numerical study is performed to estimate the sensitivity to geometrical parameters. For this reason, not only effective elastic properties but also effective thermal expansion coefficients are evaluated. Numerical tests performed on simplified μCT (computational microtomography) samples, again with the help of XFEM, serve as an additional source of information for the validation of the proposed homogenization strategy.