The white material you are observing on the undersides of the leaves a type of soft scale insect infestation called cottony camellia scale. These insects feed on the the plant sap and produce a sticky excrement called honeydew, which serves as a substrate for the growth of sooty mold (the dark substance you see on the upper leaf surfaces). Here is our page about cottony camellia scale and recommendations for management. https://extension.umd.edu/hgic/topics/cottony-camellia-scale-shrubs

You can apply a horticultural oil spray at the dormant rate to treat this scale. You can find horticultural oil in garden centers or the garden section of some hardware stores. Read and follow the product label instructions carefully. At this time of year, you will want to pay attention to the instructions about temperature. For example, the label may recommend that the temperature remain above freezing for 24 hours after application. You may need to wait until spring.

Scale insects are notoriously difficult to control. Pruning out some of the heavily damaged portions of the shrub can also help, in addition to the use of horticultural oil. Hollies can be lightly pruned at this time of year, but for more heavy pruning of evergreens, wait until early spring.

Christa