Foraminifera are single-celled marine organisms that construct shells that remain as fossils in the marine sediments. Classifying and counting these fossils are important in paleo-oceanographic and -climatological research. However, the identification and counting process has been performed manually since the 1800s and is laborious and time-consuming. In this work, we present a deep learning-based instance segmentation model for classifying, detecting, and segmenting microscopic foraminifera. Our model is based on the Mask R-CNN architecture, using model weight parameters that have learned on the COCO detection dataset. We use a fine-tuning approach to adapt the parameters on a novel object detection dataset of more than 7000 microscopic foraminifera and sediment grains. The model achieves a (COCO-style) average precision of 0.78 on the classification and detection task, and 0.80 on the segmentation task. When the model is evaluated without challenging sediment grain images, the average precision for both tasks increases to 0.84 and 0.86, respectively. Prediction results are analyzed both quantitatively and qualitatively and discussed. Based on our findings we propose several directions for future work and conclude that our proposed model is an important step towards automating the identification and counting of microscopic foraminifera.