Just to clarify, it's not greens that appear white in IR, it's living plants that appear white because they relfect a lot of near infrared. It's totally conceivable that you can find green paint or something else that's green that appears black in IR. That's part of the fun of IR - discovering a whole new world because we're not familair with the reflectivity properties of materials in the infrared.
Color infrared photos come from a variety of factors and are often referred to as pseudo-color. When done digitally with a more shallow filter like a Hoya R72, a small amount of visible light makes it through the filter and can contribute color to an image. Also, the CCD's own RGB (or CMYG in some cases) filters pass different IR wavelengths by varying amounts causing the CCD to falsley perceive color in the infrared spectrum.
Visible light is 400 nanometers (violet) to about 700nm (red) Near-infrared is about 700nm-1200nm (which is the approximate limit of what a typical silicon based CCD will react to.)
Digital cameras have an IR blocking filter in front of the CCD so that the infrared light doesn't interfere with taking a good color photo. Because of this when using an IR filter, you often have to do long exposures (several seconds in daylight) with an unmodified camera. Some people mod their cameras and replace this IR filter with clear glass to make their camera extra sensitive to IR.
I hope this helps a bit with the background.