Matrix microcracks, which can develop in composite materials due to process induced thermal stresses, can serve not only to degrade the mechanical performance of the composite but cause its ultimate failure as well. The goal of the current investigation is to study one of the factors which influences microcracks:​ a region with its own distinct characteristics known as the interphase which exists between the fiber and matrix. By representing a fiber surrounded by an interphase as a pair of concentric cylinders in an infinite matrix containing an arbitrarily curved crack, the general problem is formulated with the Kolosov-Muskhelishvili complex stress potential technique. Modeling the crack as an unknown distribution of dislocations, the resulting Cauchy singular integral equations are solved with the LobattoChebyshev quadrature technique. After checking the accuracy of the current solution with previously published results of the crack-inclusion (no-interphase) problem, preliminary studies were conducted with a glass fiber-epoxy composite to examine the influence of the interphase on radial and circumferential matrix cracks subjected to either an external mechanical or thermal load. Results from this particular study show that variations in the interphase thickness and mechanical properties interact in a complex way to either reduce or enhance the influence of the inclusion and therefore, indicate that a properly tailored interphase could be used to reduce microcracking.