Continuous fiber reinforced ceramic composites (CFCCs) are widely used in high performance and high temperature applications. The behavior of CFCCs under various conditions is not easily predicted. Micromechanical modeling of CFCCs using a representative volume element (RVE) approach provides useful prediction of the composite behavior. Conventionally, the effect of fiber-matrix interface on effective property prediction of the CFCCs is not considered in the micromechanical modeling approach. In the current work, a comprehensive three-dimensional micromechanical modeling procedure is proposed for effective elastic behavior estimation of CFCCs. Application of the micromechanical model for various interfaces has been considered to evaluate the effect of different interfaces and highlight the applicability of current model. Cohesive damage modeling approach is used to model the crack growth along with fiber bridging. The finite element model is validated by comparing with available data in the literature.