American Airlines, Iberia, British Airways, Finnair and various other airlines have round-trip flights from Austin (AUS) to Madrid (MAD) for $540-$549 with a connection. Flights January, February, March, October, and November. Departures on Monday, Tuesday, Wednesday, and Sunday. 7-day minimum stay required. No Thanksgiving dates.
Flight may operate as an American/Oneworld code-share. So (Iberia, BA, Finnair, etc, may be the operator of the flight.)