Unified Multimodal Models (UMMs) offer powerful cross-modality capabilities but introduce new safety risks not observed in single-task models. Despite their emergence, existing safety benchmarks remain fragmented across tasks and modalities, limiting the comprehensive evaluation of complex system-level vulnerabilities. To address this gap, we introduce UniSAFE, the first comprehensive benchmark for system-level safety evaluation of UMMs across 7 I/O modality combinations, spanning conventional tasks and novel multimodal-context image generation settings. UniSAFE is built with a shared-target design that projects common risk scenarios across task-specific I/O configurations, enabling controlled cross-task comparisons of safety failures. Comprising 6,802 curated instances, we use UniSAFE to evaluate 15 state-of-the-art UMMs, both proprietary and open-source. Our results reveal critical vulnerabilities across current UMMs, including elevated safety violations in multi-image composition and multi-turn settings, with image-output tasks consistently more vulnerable than text-output tasks. These findings highlight the need for stronger system-level safety alignment for UMMs. Our code and data are publicly available at https://github.com/segyulee/UniSAFE