The reason you can see the dark side of the moon is [Earthshine](https://en.wikipedia.org/wiki/Planetshine). Sunlight hits the Earth, some of which gets reflected off, which hits the moon and then gets reflected back to the Earth.
And just in case it’s not obvious, the moon is not transparent during the day. The atmosphere is in front of the moon, so the blue light it scatters obscures anything less bright than it.
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