We propose and demonstrate a novel machine learning algorithm that assesses pulmonary edema severity from chest radiographs. While large publicly available datasets of chest radiographs and free-text radiology reports exist, only limited numerical edema severity labels can be extracted from radiology reports. This is a significant challenge in learning such models for image classification. To take advantage of the rich information present in the radiology reports, we develop a neural network model that is trained on both images and free-text to assess pulmonary edema severity from chest radiographs at inference time. Our experimental results suggest that the joint image-text representation learning improves the performance of pulmonary edema assessment compared to a supervised model trained on images only. We also show the use of the text for explaining the image classification by the joint model. To the best of our knowledge, our approach is the first to leverage free-text radiology reports for improving the image model performance in this application. Our code is available at: https://github.com/RayRuizhiLiao/joint_chestxray.