Breastmilk Stains?

My breastmilk stains all my clothes unless I use nursing pads (which requires I wear a bra full time). Whatever breast doesn't have a baby latched just dumps milk when he's nursing and it soaks everything, leaving stains. On most clothes they're just dark patches, but on anything white or beige, our detergent turns them grey. Is it normal for breastmilk to stain clothing? What, if anything, can I do to remove these stains?