Even in the era of precision medicine, with various molecular tests based on omics technologies available to improve the diagnosis process, microscopic analysis of images derived from stained tissue sections remains crucial for diagnostic and treatment decisions. Among other cellular features, both nuclei number and shape provide essential diagnostic information. With the advent of digital pathology and emerging computerized methods to analyze the digitized images, nuclei detection, their instance segmentation and classification can be performed automatically. These computerized methods support human experts and allow for faster and more objective image analysis. While methods ranging from conventional image processing techniques to machine learning-based algorithms have been proposed, supervised convolutional neural network (CNN)-based techniques have delivered the best results. In this paper, we propose a CNN-based dual decoder U-Net-based model to perform nuclei instance segmentation in hematoxylin and eosin (H&E)-stained histological images. While the encoder path of the model is developed to perform standard feature extraction, the two decoder heads are designed to predict the foreground and distance maps of all nuclei. The outputs of the two decoder branches are then merged through a watershed algorithm, followed by post-processing refinements to generate the final instance segmentation results. Moreover, to additionally perform nuclei classification, we develop an independent U-Net-based model to classify the nuclei predicted by the dual decoder model. When applied to three publicly available datasets, our method achieves excellent segmentation performance, leading to average panoptic quality values of 50.8%, 51.3%, and 62.1% for the CryoNuSeg, NuInsSeg, and MoNuSAC datasets, respectively. Moreover, our model is the top-ranked method in the MoNuSAC post-challenge leaderboard.