Looks like it could be Alien Encounters, a docudrama aired on Discovery Science between 2012 and 2014.
Alien Encounters is a docudrama revolving around an alien space ship that was spotted traveling to earth for unknown reasons. Throughout the episodes, we are presented with the fictitious but all too familiar documentary style scientific details of our technologies, alien technologies and how this encounter develops.
The ship's interior was black, with a lot of fragmented sharp edges and a lot of green glowing lights everywhere.
The video below has a couple of "robot exploring the ship" scenes, with a glowing green structure-thingy (at 0'20 and 1'48). Here's a screenshot with the black sharp edges.
Some kind of series of events reveals that the ship isn't piloted by aliens, it is the alien.
The series apparently focuses on the relationships between biology and technology; especially, the ship is rumored to be the combination of both, as pointed out by these two quotes from the video above:
Signs of life... I think it's very likely that an advanced civilization would combine the advantages of machines with the advantages of biological systems. (timestamp: 0'32)
Could this alien species have gone from the same transformation? Did this great living machine have organic origins? (timestamp: 2'55)
Activating this light causes a vast amount of black spheres to appear on Earth that then slowly break apart into smaller and smaller spheres.
Wikipedia mentions, in the second season:
Episode 1: Alien spacecrafts deposit thousands of pods on the Earth's surface.
Episode 2: Humans learn to coexist with the ever shrinking multiplying alien pods.
And here's a picture of the spheres:
I found it by Googling
discovery channel alien spaceship orbiting earth, which returned Alien Planet. It wasn't the one, but as it was labeled "docufiction", I searched for
discovery channel docu fiction alien ship, and Alien Encounters was in the top three results.