Security Experts: Ubuntu Booted Using Parallels On an OSX System?

[Sage]

I think it would be completely naive to think there are not back doors in all the closed source operating systems.

I'm looking to move toward Ubuntu for all communications for just such a reason.  I'm using Parallels on a Mac OSX to duel boot Ubuntu.

My question to security experts:

Do I lose any protection from key loggers and back doors if OSX is booted at the same time I'm running Ubuntu in Parallels?

[b!z]

Malware inside a vm should not be able to escape.

[Sage]

If I have a keylogger on the Mac OS will it be able to capture keystrokes in the Ubuntu window?

What about a keylogger sending screen captures?  Won't it be able to capture the entire screen (including the Ubuntu VHM?)