We propose a new framework, PlasmodiumVF-Net, to analyze thick smear microscopy images for a malaria diagnosis on both image and patient-level. Our framework detects whether a patient is infected, and in case of a malarial infection, reports whether the patient is infected by Plasmodium falciparum or Plasmodium vivax. PlasmodiumVF-Net first detects candidates for Plasmodium parasites using a Mask Regional-Convolutional Neural Network (Mask R-CNN), filters out false positives using a ResNet50 classifier, and then follows a new approach to recognize parasite species based on a score obtained from the number of detected patches and their aggregated probabilities for all of the patient images. Reporting a patient-level decision is highly challenging, and therefore reported less often in the literature, due to the small size of detected parasites, the similarity to staining artifacts, the similarity of species in different development stages, and illumination or color variations on patient-level. We use a manually annotated dataset consisting of 350 patients, with about 6000 images, which we make publicly available together with this manuscript. Our framework achieves an overall accuracy above 90% on image and patient-level.