State-of-the-art ontology languages are often not sufficiently expressive to accurately represent domains consisting of objects connected in a complex way. As a possible remedy, in our previous work we have proposed an extension of ontology languages with description graphs. In this paper, we extend this formalism by allowing for multiple graphs that can be combined in complex ways, thus obtaining a powerful language for modeling structured objects. By imposing a particular acyclicity restriction on the relationships between the graphs, we ensure that checking satisfiability of knowledge bases expressed in our language is decidable. We also present a practical reasoning algorithm.