Medical foundation models show promise to learn broadly generalizable features from large, diverse datasets. This could be the base for reliable cross-modality generalization and rapid adaptation to new, task-specific goals, with only a few task-specific examples. Yet, evidence for this is limited by the lack of public, standardized, and reproducible evaluation frameworks, as existing public benchmarks are often fragmented across task-, organ-, or modality-specific settings, limiting assessment of cross-task generalization. We introduce UNICORN, a public benchmark designed to systematically evaluate medical foundation models under a unified protocol. To isolate representation quality, we built the benchmark on a novel two-step framework that decouples model inference from task-specific evaluation based on standardized few-shot adaptation. As a central design choice, we constructed indirectly accessible sequestered test sets derived from clinically relevant cohorts, along with standardized evaluation code and a submission interface on an open benchmarking platform. Performance is aggregated into a single UNICORN Score, a new metric that we introduce to support direct comparison of foundation models across diverse medical domains, modalities, and task types. The UNICORN test dataset includes data from more than 2,400 patients, including over 3,700 vision cases and over 2,400 clinical reports collected from 17 institutions across eight countries. The benchmark spans eight anatomical regions and four imaging modalities. Both task-specific and aggregated leaderboards enable accessible, standardized, and reproducible evaluation. By standardizing multi-task, multi-modality assessment, UNICORN establishes a foundation for reproducible benchmarking of medical foundation models. Data, baseline methods, and the evaluation platform are publicly available via unicorn.grand-challenge.org.