Assuras attended London Central Secondary School. She remained in London to attend the University of Western Ontario (UWO), pursuing a B.Sc (Honours) degree with the intent of going into medicine. She graduated in 1980, but in a change of career plans entered the graduate program in journalism and earning her master's degree in 1981. Twenty-one years later she commented on the impact the journalism program had on her:

Assuras has worked for CITY-TV and Global Television, including a stint as reporter and weekend anchor for CityPulse from 1985 to 1988.

From 1992 to 1993 she worked for CTV, anchoring Canada AM. She then moved to ABC, and in May 1993, joined Aaron Brown as co-anchor of World News Now. She shared that late-night anchor desk with Boyd Matson, fellow Canadian Kevin Newman, and Mark Mullen before leaving the show in January 1997.

In 1997 she moved to CBS, first joining CBS Eye On People, a cable network that CBS launched in March 1997. She also worked as a national correspondent and later became co-anchor of The Saturday Early Show and then the CBS Evening News Saturday (in an alternating arrangement with Russ Mitchell).

Milwaukee-based rock group, "The Mosleys" wrote a song about her called "Thalia".

In a June 22, 1998 article in Maclean's, Assuras commented on her reason for moving to the United States:

On Saturday, April 2, 2005, Assuras anchored CBS's extensive breaking-news coverage of the death of Pope John Paul II.

Along with a number of notable Greek Americans, she is a member of the advisory board of The Next Generation Initiative, a leadership program aimed at getting students involved in public affairs.

On July 31, 2009, CBS announced they would not renew Assuras's contact for a 13th year. Her future plans were not imemdiately known.

The Daughters of Penelope recognized Assuras with the "2000 Salute to Women" award; She was awarded the Marie Torre Memorial Award in 2001.