In this paper, we develop techniques for interoperable query processing between object and relational schemas. The objective is to pose a query against a local object schema and be able to share information transparently from target relational databases. Our approach is a mapping approach (as opposed to a global schema approach) and is based on using canonical representations (CR). We use one CR for resolving heterogeneity based on the object and relational query languages. We use a second parameterized CR to resolve representational heterogeneity between object and relational schema, and to build a mapping knowledge dictionary. There is also a set of mapping rules, based on the parameters of the CR, which defines the appropriate mapping between schemas. A query posed against the local object schema is first represented in the CR for queries, and then transformed by the mapping rules, to an appropriate query for the target relational schema, using relevant information from the mapping knowledge dictionary. The use of the parameterized CR allows us to build the mapping knowledge dictionary easily, and allows reusability of the mapping rules.