Mold and mildew feed on organic substances. Latex is more resistant to fungus than oils are, but both will support it's growth.
For repainting, Zinnser (the manufacturer of BIN primer) makes two grades of a mildew resisitant paint, both called PermaWhite (can be tinted!), one for interior, the other for exterior. I've used both with excellent results. It will definatly deal with the mildew on a long terma basis.
One note is that PermaWhite isn't suitabe for floors.