I agree fully with @a crazy Minon's answer. I will just slightly expand on it and provide a couple of additional references.
While Dice is a popular metric for evaluating segmentation, it is certainly not the only one. You are right in thinking that pixel accuracy is a poor choice of evaluation metric. The main issue is that it performs poorly when when there is class imbalance, which is often the case in imaging data.
I will add that Intersection over Unions (IoU) is another metric that is frequently employed to evaluate segmentation performance. It is also known as the Jaccard Index. The articles "Metrics to Evaluate your Semantic Segmentation Model" and "All the segmentation metrics!" provide good simplified introductions to various commonly used segmentation metrics. While Dice and IoU are similar and are positively correlated, they are not equivalent, as explained by this StackOverflow answer. New metrics are also being developed--such as the Boundary Jaccard--to overcome limitations of current metrics, and comparisons of these metrics have been published for specific applications (see example ref, which lists 33 evaluation metrics for segmentation in Table 1).
Finally, if your interest is really for one class, then accuracy, sensitivity, and specificity for segmenting that class alone can be useful metrics.
The powers that be at your institution are wise in asking for multiple evaluation metrics because each metric has its limitations and no single metric can fully capture the performance of a segmentation network.