Understanding of the coupled effects of aggregates and interfacial transition zones (ITZs) on hydraulic transport properties of unsaturated cementitious composites (CC) is of great importance for the design of CC durability. In this work, a comprehensive micromechanical theoretical framework is devised for the accurate predictions of the effective hydraulic conductivity, diffusivity and sorptivity of saturated and unsaturated CC, in which CC are regarded as a three-phase structure consisting of spheroidal aggregates with a certain gradation, their surrounding permeable ITZs with a specific thickness, and homogeneous cement paste at a mesoscopic level. Comparisons against experimental, numerical and analytical data suggest that the proposed framework is a reliable means to predict these effective hydraulic transport properties. The micromechanical framework can be regarded as a generic model that suits for predicting other hydraulic-like transport properties of multiphase composites not limited to cementitious composites involving spheroidal inhomogeneities and their surrounding interphase. This framework sheds light on the coupled effects of properties of aggregates (shape, gradation, mean size, and volume fraction) and ITZ (volume fraction, thickness, and hydraulic properties) on the effective hydraulic transport properties of CC. The results elucidate the complex relationship of components-structures-transport properties, which in turn can provide insights for understanding degradation of concrete in practical applications.