We investigate the possibility of using structured data to improve search over unstructured documents. In particular, we use relevance feedback to create a `virtuous cycle' between structured data gathered from the Semantic Web and web-pages gathered from the hypertext Web. Previous approaches have generally considered searching over the Semantic Web and hypertext Web to be entirely disparate, indexing and searching over different domains. Our novel approach is to use relevance feedback from hypertext Web results to improve Semantic Web search, and results from the Semantic Web to improve the retrieval of hypertext Web data. In both cases, our evaluation is based on certain kinds of informational queries (abstract concepts, people, and places) selected from a real-life query log and checked by human judges. We show our relevance model-based system is better than the performance of real-world search engines for both hypertext and Semantic Web search, and we also investigate Semantic Web inference and pseudo-relevance feedback.