State of the art formalisms for distributed ontology integration provide ways to express semantic relations between homogeneous components of different ontologies; namely, they allow to map concepts into concepts, individuals into individuals, and properties into properties. However, the extensive usage of multiple distributed ontologies requires the capability for expressing different forms of mappings, which extend the semantic relations among homogeneous components studied so far. In recent papers extensions of the Distributed Description Logic (DDL) have been proposed to represent mappings between heterogeneous elements; i.e. mappings connecting concepts and relations. In this paper we investigate the computational properties of reasoning with mappings between homogeneous as well as heterogeneous elements in distributed ontologies, and an effective decision procedure for reasoning with multiple ontologies bridged with both forms of mappings.