Topological relationship is a very important spatial relationship in geographical information systems (GIS). During the past decades, many models that distinguish topological relationships have been proposed. But these models cannot distinguish the topological relationships between heterogeneous geometrycollection objects, which are composed of different dimensional geometries. We introduce the formal definition of mixed geometry and regularization rules. Base on the spatial model and Dimensionally Extended Nine-Intersection Model (DE-9IM), we propose a topological relationship model—Integrated Dimensionally Extended Nine-Intersection Model (IDE-9IM). The model can distinguish not only the topological relationships between single points, lines, areas, and/or homogeneous geometrycollection objects, but also the topological relationships between heterogeneous geometrycollection objects by considering the whole objects and the components of the complex objects. So IDE-9IM can be taken as a unified model of distinguishing topological relationships between arbitrary spatial objects.