Bidirectional (or "bidi") means "A writing system in which text is generally flush right, and most characters are written from right to left, but some text is written left-to-right as well. Arabic and Hebrew are the only bidirectional writing systems in current use." (MultiLingual)
Text with both left-to-right and right-to-left is bidirectional.
MultiLingual. 2007. "Glossary." 2007 Resource Directory. http://www.multilingual.com/resourceDirectory/
Wikipedia, "Bi-directional text," http://en.wikipedia.org/wiki/Bi-directional_text