Given a music recording, music structure analysis aims at identifying important structural elements and segmenting the recording according to these elements. In jazz music, a performance is often structured by repeating harmonic schemata (known as choruses), which lay the foundation for improvisation by soloists. Within the fields of music information retrieval (MIR) and computational musicology, the Weimar Jazz Database (WJD) has turned out to be an extremely valuable resource for jazz research. Containing high-quality solo transcriptions for 456 solo sections, the dataset opened up new avenues for the understanding of creative processes in jazz improvisation using computational methods. In this paper, we complement this dataset by introducing the Jazz Structure Dataset (JSD), which provides annotations on structure and instrumentation of entire recordings. The JSD comprises 340 recordings with more than 3000 annotated segments, along with a segment-wise encoding of the solo and accompanying instruments. These annotations provide the basis for training, testing, and evaluating models for various important MIR tasks, including structure analysis, solo detection, or instrument recognition. As an example application, we consider the task of structure boundary detection. Based on a traditional novelty-based as well as a more recent data-driven approach using deep learning, we indicate the potential of the JSD while critically reflecting on some evaluation aspects of structure analysis. In this context, we also demonstrate how the JSD annotations and analysis results can be made accessible in a user-friendly way via web-based interfaces for data inspection and visualization. All annotations, experimental results, and code for reproducibility are made publicly available for research purposes.