Cell or nucleus detection is a fundamental task in microscopy image analysis and has recently achieved state-of-the-art performance by using deep neural networks. However, training supervised deep models such as convolutional neural networks (CNNs) usually requires sufficient annotated image data, which is prohibitively expensive or unavailable in some applications. Additionally, when applying a CNN to new datasets, it is common to annotate individual cells/nuclei in those target datasets for model re-learning, leading to inefficient and low-throughput image analysis. To tackle these problems, we present a bidirectional, adversarial domain adaptation method for nucleus detection on cross-modality microscopy image data. Specifically, the method learns a deep regression model for individual nucleus detection with both source-to-target and target-to-source image translation. In addition, we explicitly extend this unsupervised domain adaptation method to a semi-supervised learning situation and further boost the nucleus detection performance. We evaluate the proposed method on three cross-modality microscopy image datasets, which cover a wide variety of microscopy imaging protocols or modalities, and obtain a significant improvement in nucleus detection compared to reference baseline approaches. In addition, our semi-supervised method is very competitive with recent fully supervised learning models trained with all real target training labels.