Emily -
Great question! I had to look it up myself!
Yes, the astronauts on the International Space Station are in solar storms
from time to time. For example, October 2005, the sun was extremely active
and pelted the earth for weeks. NASA monitors the radiation levels to make sure that its
safe enough, and the hull of the ISS does a pretty good job shielding the astronauts
from the protons etc. Amazingly, the magnetic fields in a CME actually cause a drop in cosmic
rays for the astronauts. So, in a sense, being inside a CME is a good thing!
- Peter