The family of an American killed in the crash of Malaysia Airlines Flight MH17 filed an antiterrorism lawsuit Thursday alleging that two prominent U.S. money transfer companies and two Russian banks were responsible for providing financial support to the pro-Russian separatists involved in the destruction of the plane.

Quinn Lucas Schansman, a dual U.S.-Dutch citizen, was one of 298 people killed in 2014 when a Boeing 777 aircraft was hit by a Russian-made antiaircraft missile in Ukrainian airspace while flying a route from...