Omni-modal large language models (OLLMs) aim to unify audio, vision, and text understanding within a single framework. While existing benchmarks primarily evaluate general cross-modal question-answering ability, it remains unclear whether OLLMs achieve modality-invariant reasoning or exhibit modality-specific biases. We introduce XModBench, a large-scale tri-modal benchmark explicitly designed to measure cross-modal consistency. XModBench comprises 60,828 multiple-choice questions spanning five task families and systematically covers all six modality compositions in question-answer pairs, enabling fine-grained diagnosis of an OLLM's modality-invariant reasoning, modality disparity, and directional imbalance. Experiments show that even the strongest model, Gemini 2.5 Pro, (i) struggles with spatial and temporal reasoning, achieving less than 60% accuracy, (ii) reveals persistent modality disparities, with performance dropping substantially when the same semantic content is conveyed through audio rather than text, and (iii) shows systematic directional imbalance, exhibiting lower consistency when vision serves as context compared to text. These findings indicate that current OLLMs remain far from truly modality-invariant reasoning and position XModBench as a fundamental diagnostic tool for evaluating and improving cross-modal competence. All data and evaluation tools will be available at https://xingruiwang.github.io/projects/XModBench/.