answer
****SPOILER*****
Also, some additional parts are in shadow because of the irregularity of surface features, such as craters and mountains which cast shadows.
answer
****SPOILER*****
This is much more complicated than I thought when I posted this poll. It also depends on how you measure the "surface", i.e., if you measue the entire surface as a smooth sphere or as a fractal surface.
See: https://en.wikipedia.org/wiki/Fractal_dimension
and
https://en.wikipedia.org/wiki/Surface_roughness#Soil-surface_roughness
answer
****SPOILER*****
Excluding light from sources other than directly from the Sun, it's between 85-90% in shadow. The entire back of the moon is in the shadow of the moon itself, while the front is about 75% covered by the shadow of the Earth.