We are concerned with the challenge of coronavirus disease (COVID-19) detection in chest X-ray and Computed Tomography (CT) scans, and the classification and segmentation of related infection manifestations. Even though it is arguably not an established diagnostic tool, using machine learning-based analysis of COVID-19 medical scans has shown the potential to provide a preliminary digital second opinion. This can help in managing the current pandemic, and thus has been attracting significant research attention. In this research, we propose a multi-task pipeline that takes advantage of the growing advances in deep neural network models. In the first stage, we fine-tuned an Inception-v3 deep model for COVID-19 recognition using multi-modal learning, i.e., using X-ray and CT scans. In addition to outperforming other deep models on the same task in the recent literature, with an attained accuracy of 99.4%, we also present comparative analysis for multi-modal learning against learning from X-ray scans alone. The second and the third stages of the proposed pipeline complement one another in dealing with different types of infection manifestations. The former features a convolutional neural network architecture for recognizing three types of manifestations, while the latter transfers learning from another knowledge domain, namely, pulmonary nodule segmentation in CT scans, to produce binary masks for segmenting the regions corresponding to these manifestations. Our proposed pipeline also features specialized streams in which multiple deep models are trained separately to segment specific types of infection manifestations, and we show the significant impact that this framework has on various performance metrics. We evaluate the proposed models on widely adopted datasets, and we demonstrate an increase of approximately 4% and 7% for dice coefficient and mean intersection-over-union (mIoU), respectively, while achieving 60% reduction in computational time, compared to the recent literature.