We present PosterIQ, a design-driven benchmark for poster understanding and generation, annotated across composition structure, typographic hierarchy, and semantic intent. It includes 7,765 image-annotation instances and 822 generation prompts spanning real, professional, and synthetic cases. To bridge visual design cognition and generative modeling, we define tasks for layout parsing, text-image correspondence, typography/readability and font perception, design quality assessment, and controllable, composition-aware generation with metaphor. We evaluate state-of-the-art MLLMs and diffusion-based generators, finding persistent gaps in visual hierarchy, typographic semantics, saliency control, and intention communication; commercial models lead on high-level reasoning but act as insensitive automatic raters, while generators render text well yet struggle with composition-aware synthesis. Extensive analyses show PosterIQ is both a quantitative benchmark and a diagnostic tool for design reasoning, offering reproducible, task-specific metrics. We aim to catalyze models' creativity and integrate human-centred design principles into generative vision-language systems.