This paper presents our research on developing an ontology-based framework that can represent morphological characteristics related to assembly joints. Joints within the physical structure of an assembly are inevitable because of the limitations of component geometries and the associated, required engineering properties. Consequently, a framework is needed that can capture and propagate assembly design and joint information in a robust assembly model throughout the entire product development processes. The framework and model are based on an understanding of the morphological characteristics of an assembly and its different physical effects. The morphological characteristics are consequences of the principal physical processes and of the design intentions. Therefore, the morphological characteristics should be carefully represented while considering the geometry and topology of assembly joints. In this research, assembly joint topology is defined by a mereotopology, which is a region-based theory for the parts and associated concepts. This formal ontology can differentiate often ambiguous assembly and joining relations. Furthermore, the mereotopological definitions for assembly joints are implemented in Semantic Web Rule Language (SWRL) rules and Web Ontology Language triples. This process provides universality to the mereotopological definitions. Two geometrically and topologically similar joint pairs are presented to describe how the assembly joints can be defined in mereotopology and be transformed into SWRL rules. Web3D is also employed to support network-enabled sharing of assembly geometry. Finally, the proposed modeling framework is demonstrated using a real fixture assembly. This case study demonstrates the usability of the proposed framework for network-based design collaboration.