The two hemi-spheres are the Plenaria of the Senate and the Federal Chamber.
The hemi-shpere looking down is the Senate, and the other one is the Chamber. Why that? According to Niemeyer, the Senate is by nature more conservative, whereas the Chamber is more opened to the popular clamor; so, the Senate was built more hermetic, and the Chamber more opened. Also, because the Senate and the Chamber have complementary functions, they were also shaped in a complementary way (each House could be stacked on top of the other).
The two buildings in between the hemi-spheres are called Annex I and this is where part of the administrative staff of the Congress is located. These are the two tallest buildings in the Federal District.
If the doors of this building were locked it would become the prision with the most dangerous criminals in this country. About 1/3 of deputies and senators are under investigation. The other 2/3 aren't - yet.