As of yet, I can only think of one way to get a virus to work on both operating systems; using Wine in Linux. Early in their development, they actually listed a known Windows virus as executing (but not redistributing) in Wine.
The short answer is no, not easily. Most Linus distributions come with clamav now, and it does a decent job detecting viruses. I even have an email filter set up so when my mother receives a questionable email, she can forward it to me with a specific subject, and my computer will scan it and return the results.
Just make sure to read up on the antivirus utilities you install on both OS's, and keep them up to date.