This study concerns uncertainty quantification (UQ) in homogenizing the specific fiber-reinforced composite. This composite exhibits a lack of perfect connection between the fiber and the matrix due to some stochastic discontinuities at the interface. Thanks to specific statistical geometrical modeling of these defects, they are incorporated into the homogenization procedure. They are inserted into the new artificial material called interphase separating the matrix and the fibers. The random elastic modulus of this new material is calculated via probabilistic averaging of the matrix and the defects. The uncertainty quantification in this problem is carried out using three classical concurrent techniques—Monte–Carlo simulation, semi-analytical approach, and also the generalized iterative stochastic perturbation method. All these numerical methods have been implemented using the Finite Element Method (FEM) homogenization-oriented code Monte–Carlo Effective Constants (MCCEFF) and the symbolic computer algebra system MAPLE. The alternative approach of uncertainty propagation is delivered using the determination of the Shannon entropy and its fluctuations, and also by Bhattacharyya relative entropy. These entropies’ variations in addition to the input coefficient of variation of the defects and their size have been determined and discussed here.