Task interference, the performance degradation caused by task switches within a single conversation, has been studied exclusively in text-only settings despite the growing prevalence of multimodal dialogue systems. We introduce a benchmark for evaluating this phenomenon in multimodal LLMs, covering six tasks across text and vision with systematic variation of history-target along three axes: modality mismatch, reasoning mismatch, and answer format mismatch. Experiments on both open-weights and proprietary models reveal that task interference is highly directional: switching from text-only to image-based targets causes severe performance drops, while the reverse transition yields minimal degradation. Interference is further amplified when mismatches co-occur across multiple dimensions, and is driven most strongly by modality differences, followed by answer format, while reasoning requirement shifts cause minimal degradation.