Here’s a fun paper that analyzes the radiation exposure of characters in The Martian. The TL;DR is that Mark Watney would have fared better than his crewmates in the Hermes.
Mars, with its thin atmosphere and lack of magnetosphere, doesn’t offer as much protection as Earth, but it’s better than nothing.
http://www.anser.org/docs/The_Radiation_Threat_to_the_Martian.pdf