When sunlight bounces off the Earth, why isn't the entire spectrum reflected rather than just the infrared portion? I've read that greenhouse gases absorb and reemit sunlight, and that the infrared portion is what bounces off Earth back to space. When sunlight bounces off the Earth, why isn't the entire spectrum reflected rather than just the infrared portion? 
 A: The reflectivity of the atmosphere, and of the surface itself, is strongly wavelength-sensitive.  So while some percentage of any given wavelength is reflected -- and some percentage is absorbed rather than transmitted, the variation over wavelength is what leads to the somewhat misleading statement you refer to.  Here's an example of atmospheric absorption, as can be seen at wikipedia

There are also curves of reflectance.  $transmittance+absorptance+reflectance = 1$, in case you were wondering :-) . 
The reason all this matters is that shorter-wave energy, e.g. visible and some UV, that is absorbed either in the atmosphere or by the ground, is re-emitted at different wavelengths in accordance with black-body theory.  In general this leads to a lot of IR-radiation, so if the atmosphere is reflective at these wavelengths, the energy is retained rather than re-emitted to space.
A: It does. Consider this: you can see the Earth from space. Therefore, not just infrared light gets reflected but also light on the visible spectrum. 
Here's a graph (by NASA) of various planet's radio emissions. The ways that Earth can release radio waves is a bit limited. Because of that, it is safe to assume that at least some come from the Sun. 

