What most horticulturalists and gardeners call mildew is actually Powdery Mildew, in the Ascomycota phylum in the Fungi Kingdom. There are several species, all pests of flowering plants, called obligate parasites. The species that affects roses is Sphaerotheca pannosa var. rosa.
The other main form of mildew is Downy Mildew, which is a member of the Oomycota phylum in the Protista Kingdom. In commercial agriculture, Downey Mildew is a particular problem for growers of potatoes, grapes and vine-type vegetables.
Mildew can thrive on any organic matter, not just living tissue, and can appear on clothing, leather, paper, and the ceilings, walls and floors of many homes.