I covered my iris bed with wood chips to keep the ground from drying out so fast. Since the rhizomes grow partly above ground, will being covered with chips harm the plants?
Your mulch is unlikely to harm your bearded (rhizomatous) irises, as long as it is less than one inch thick over the rhizome tops and allows air through. Here is some information from The Gardener’s Iris Book by William Shear: “How deep should the rhizome be set? That depends. In light-textured soils, it can be covered by as much as one inch of soil, but for average to heavier soils, the top of the rhizome is best left exposed to the healthful influences of sun and air. Remember that the rhizome is a stem, not a root, and needs to breathe!…If you do apply a mulch, it must be loose and airy, so it won’t pack down and get soggy–a sure ticket to rotting rhizomes in the spring.” Shear suggests pulling back the mulch in spring (since it is for freeze protection in his mind), but it seems to me that would defeat your purpose. You might meet both goals (moist soil and dry rhizome tops) by mulching around the irises but not right on them.