Analytical techniques for calculating fiber-matrix (F-M) interface stresses, using repeating square and diamond regular arrays, were presented for a unidirectional composite under thermomechanical loadings. An Airy's stress function micromechanics approach from the literature, developed for calculating overall composite moduli, was extended in the present study to compute F-M interface stresses for a unidirectional graphite/epoxy (AS4/3501-6) composite under thermal, longitudinal, transverse, transverse shear, and longitudinal shear loadings. Comparisons with finite element results indicated excellent agreement of the F-M interface stresses for the square array. Under thermal and longitudinal loading, the square array had the same F-M peak stresses as the diamond array. The square array predicted higher stress concentrations under transverse normal and longitudinal shear loadings than the diamond array. Under transverse shear loading, the square array had a higher shear stress concentration while the diamond array had a higher radial stress concentration. Stress concentration factors under transverse shear and longitudinal shear loadings were very sensitive to fiber volume fraction. The present analysis provides a simple way to calculate accurate F-M interface stresses for both the square and diamond array configurations.