Breast screening is an effective method to identify breast cancer in asymptomatic women; however, not all exams are read by radiologists specialized in breast imaging, and missed cancers are a reality. Deep learning provides a valuable tool to support this critical decision point. Algorithmically, accurate assessment of breast mammography requires both detection of abnormal findings (object detection) and a correct decision whether to recall a patient for additional imaging (image classification). In this paper, we present a multi-task learning approach, that we argue is ideally suited to this problem. We train a network for both object detection and image classification, based on state-of-the-art models, and demonstrate significant improvement in the recall vs no recall decision on a multi-site, multi-vendor data set, measured by concordance with biopsy proven malignancy. We also observe improved detection of microcalcifications, and detection of cancer cases that were missed by radiologists, demonstrating that this approach could provide meaningful support for radiologists in breast screening (especially non-specialists). Moreover, we argue that this multi-task framework is broadly applicable to a wide range of medical imaging problems that require a patient-level recommendation, based on specific imaging findings.