Automatic segmentation of cellular structures is an essential step in image cytology and histology. Despite substantial progress, better automation and improvements in accuracy and adaptability to novel applications are needed. In applications utilizing multi-channel immuno-fluorescence images, challenges include misclassification of epithelial and stromal nuclei, irregular nuclei and cytoplasm boundaries, and over and under-segmentation of clustered nuclei. Variations in image acquisition conditions and artifacts from nuclei and cytoplasm images often confound existing algorithms in practice. In this paper, we present a robust and accurate algorithm for jointly segmenting cell nuclei and cytoplasm using a combination of ideas to reduce the aforementioned problems. First, an adaptive process that includes top-hat filtering, Eigenvalues-of-Hessian blob detection and distance transforms is used to estimate the inverse illumination field and correct for intensity non-uniformity in the nuclei channel. Next, a minimum-error-thresholding based binarization process and seed-detection combining Laplacian-of-Gaussian filtering constrained by a distance-map-based scale selection is used to identify candidate seeds for nuclei segmentation. The initial segmentation using a local maximum clustering algorithm is refined using a minimum-error-thresholding technique. Final refinements include an artifact removal process specifically targeted at lumens and other problematic structures and a systemic decision process to reclassify nuclei objects near the cytoplasm boundary as epithelial or stromal. Segmentation results were evaluated using 48 realistic phantom images with known ground-truth. The overall segmentation accuracy exceeds 94%. The algorithm was further tested on 981 images of actual prostate cancer tissue. The artifact removal process worked in 90% of cases. The algorithm has now been deployed in a high-volume histology analysis application.