The Montreal Convention requires airlines to compensate international travelers who are injured as a result of an “accident.” If the passenger is killed, the Montreal Convention requires the airline to compensate the family members. But the Convention considers neither an airliner’s pilots nor its flight attendants to be “passengers.” Thus, crew members’ claims (or the claims of their families in the event of a fatal accident), are usually governed by by local law, not the Convention. In the US, that means that any lawsuit the crew member might bring against the airline would likely be barred by the applicable workers compensation statutes, which typically prevent any employee from suing his or her employer for work-related injuries.
Of course, crew members or their families are free to pursue claims against those other than the airline who might be responsible for an accident. Often that’s an aviation manufacturer. But unlike passengers, crew members generally cannot sue the airline.
There is one exception. A crew member may be considered a “passenger” if she was “deadheading.” That is, if the crew member was off-duty, but the airline had her on the aircraft simply to transport her from Point A to Point B, then the Convention would apply to her claims.