Determining the overlapping degree of interfaces around solids is an open problem with great significance in a variety of materials. So far, this search has been performed only on a case-by-case basis, particularly for hard spherical particles. Here, we present a generalized scheme to evaluate analytically the interfacial overlapping degree with complex convex particles. It is essentially an extension of spheres to complex convex particles like convex polyhedrons and ellipsoids for the interfacial overlapping degree. Additionally, a numerical model is also proposed to numerically derive the interfacial overlapping degree on the basis of the Minkowsky addition manner. Comparing with the theoretical data reported in the literature and numerical results from the present numerical model, the proposed theoretical scheme is confirmed with a favorable reliability. Furthermore, we find a quantitative mechanism between the interfacial overlapping degree and the surface configurations of convex particles. Such a mechanism can be used as a theoretical criterion to provide guidance for practical industries of composite media. (C) 2015 Elsevier B.V. All rights reserved.