The Moon reflects around 12% of the sunlight
Our Earth reflects about 37% of the sunlight
Venus albedo of 0.65
Mercury, at 0.11, has the lowest planetary albedo.
From:
http://www.asterism.org/tutorials/tut26-1.htm

"A lot of confusing statements are made about the albedo of the moon.
...
The original definition of albedo, proposed by Bond, is the ratio of total solar radiation scattered from a body to the radiation incident upon it. The Bond albedo of the moon is 11%. But limiting this figure to V-band radiation produces quite a different value. The average visual Bond albedo of the earth-facing side of the moon is 7.2%.
...
- something about in the middle range of lunar brightnesses is just as bright as a grassy yard at noon."
http://jeff.medkeff.com/astro/lunar/obs_tech/albedo.htm

But generally for earthlings from the surface of Earth, the Moon appears to have around .08 albedo.

Anyhow the Moon is more of a black body than Earth is, or it's sometimes said Earth is a grey body, so the Moon is a much darker gray body than Earth. And in same way Venus is much whiter gray body as compared to Earth.

Now, all of the energy from the Sun which shines on the Moon is radiated back into Space, but the vast majority of this energy is not reflected, but is radiated back as infrared.

The intensity of moonlight that reaches Earth is supposed to be around 1/400,000th of amount from the Sun, but I assume they mean visible light. And I assume they mean the visible light that gets through the Earth atmosphere.

But my question is how much infrared energy gets to Earth [it's upper atmosphere] which is from the Moon?
If the Moon was a smooth white sphere, we would receive more than ten times the visible light from it. And the Moon would not get as warm and we would receive less infrared from it- though still a fair amount.

Imagine if the Moon was molten aluminum [shiny stuff] it would be almost a bright as the Sun- though the area which was as bright as the sun would a small part of the Moon. If you had a round mirror the same size as the Moon [not a sphere, but flat] you could reflect around the same sunlight power as the Sun does on Earth but in a small area [the area of the Moon, so something the size of the US could kept lit in sunlight. If you curved this mirror slightly you increase the area to cover the entire Earth [though the energy from it wouldn't increase- you get less energy per square meter falling on Earth]. The Moon surface is more curved than you would need curve the mirror to cover entire 1/2 facing side of Earth, therefore the total amount of infrared radiation that could possibly reach Earth would be less than this. But if you painted the Moon the brightest white or covered with alumimun foil the amount of visible light that reached Earth would less energy than the amount of infrared energy currently reaching Earth.

So, I don't know how much infrared is reaching Earth from the Moon, but seems like it could be significant.