For large-scale vision tasks in biomedical images, the labeled data is often limited to train effective deep models. Active learning is a common solution, where a query suggestion method selects representative unlabeled samples for annotation, and the new labels are used to improve the base model. However, most query suggestion models optimize their learnable parameters only on the limited labeled data and consequently become less effective for the more challenging unlabeled data. To tackle this, we propose a two-stream active query suggestion approach. In addition to the supervised feature extractor, we introduce an unsupervised one optimized on all raw images to capture diverse image features, which can later be improved by fine-tuning on new labels. As a use case, we build an end-to-end active learning framework with our query suggestion method for 3D synapse detection and mitochondria segmentation in connectomics. With the framework, we curate, to our best knowledge, the largest connectomics dataset with dense synapses and mitochondria annotation. In this new dataset, our method outperforms previous state-of-the-art methods by 3.1% for synapse and 3.8% for mitochondria in terms of region-of-interest proposal accuracy. We also apply our method to image classification, where it outperforms previous approaches on CIFAR-10 under the same limited annotation budget.