Information extraction from chemistry literature is vital for constructing up-to-date reaction databases for data-driven chemistry. Complete extraction requires combining information across text, tables, and figures, whereas prior work has mainly investigated extracting reactions from single modalities. In this paper, we present OpenChemIE to address this complex challenge and enable the extraction of reaction data at the document level. OpenChemIE approaches the problem in two steps: extracting relevant information from individual modalities and then integrating the results to obtain a final list of reactions. For the first step, we employ specialized neural models that each address a specific task for chemistry information extraction, such as parsing molecules or reactions from text or figures. We then integrate the information from these modules using chemistry-informed algorithms, allowing for the extraction of fine-grained reaction data from reaction condition and substrate scope investigations. Our machine learning models attain state-of-the-art performance when evaluated individually, and we meticulously annotate a challenging dataset of reaction schemes with R-groups to evaluate our pipeline as a whole, achieving an F1 score of 69.5%. Additionally, the reaction extraction results of \ours attain an accuracy score of 64.3% when directly compared against the Reaxys chemical database. We provide OpenChemIE freely to the public as an open-source package, as well as through a web interface.