As vision-language models (VLMs) become increasingly capable, maintaining a balance between safety and usefulness remains a central challenge. Safety mechanisms, while essential, can backfire, causing over-refusal, where models decline benign requests out of excessive caution. Yet, there is currently a significant lack of benchmarks that have systematically addressed over-refusal in the visual modality. This setting introduces unique challenges, such as dual-use cases where an instruction is harmless, but the accompanying image contains harmful content. Models frequently fail in such scenarios, either refusing too conservatively or completing tasks unsafely, which highlights the need for more fine-grained alignment. The ideal behaviour is safe completion, i.e., fulfilling the benign parts of a request while explicitly warning about any potentially harmful elements. To address this, we present DUAL-Bench, a large scale multimodal benchmark focused on over-refusal and safe completion in VLMs. We evaluated 18 VLMs across 12 hazard categories under semantics-preserving visual perturbations. In dual-use scenarios, models exhibit extremely fragile safety boundaries. They fall into a binary trap: either overly sensitive direct refusal or defenseless generation of dangerous content. Consequently, even the best-performing model GPT-5-Nano, at just 12.9% safe completion, with GPT-5 and Qwen families averaging 7.9% and 3.9%. We hope DUAL-Bench fosters nuanced alignment strategies balancing multimodal safety and utility. Content Warning: This paper contains examples of sensitive and potentially hazardous content.