Background The prognosis, diagnosis, and treatment of many genetic disorders and familial diseases significantly improve if the family history (FH) of a patient is known. Such information is often written in the free text of clinical notes. Objective The aim of this study is to develop automated methods that enable access to FH data through natural language processing. Methods We performed information extraction by using transformers to extract disease mentions from notes. We also experimented with rule-based methods for extracting family member (FM) information from text and coreference resolution techniques. We evaluated different transfer learning strategies to improve the annotation of diseases. We provided a thorough error analysis of the contributing factors that affect such information extraction systems. Results Our experiments showed that the combination of domain-adaptive pretraining and intermediate-task pretraining achieved an F1 score of 81.63% for the extraction of diseases and FMs from notes when it was tested on a public shared task data set from the National Natural Language Processing Clinical Challenges (N2C2), providing a statistically significant improvement over the baseline (P<.001). In comparison, in the 2019 N2C2/Open Health Natural Language Processing Shared Task, the median F1 score of all 17 participating teams was 76.59%. Conclusions Our approach, which leverages a state-of-the-art named entity recognition model for disease mention detection coupled with a hybrid method for FM mention detection, achieved an effectiveness that was close to that of the top 3 systems participating in the 2019 N2C2 FH extraction challenge, with only the top system convincingly outperforming our approach in terms of precision.