Iberia flights are an option for awards on American Airlines miles, but they weren't showing on aa.com . The best option to find availability was on the British Airways site with a login in their program, and you were advised to search one flight segment at a time, then call AA to book.
Now One Mile at a Time post: Iberia flights are starting to be loaded as awards that can be searched and booked on aa.com . Often when searching awards there, most of the availability is on British Airways, which has carrier-imposed surcharges that make it not worth considering for a "free" flight. Iberia's surcharges are modest, and this makes it easier to find transatlantic trips where AA miles are usable.
Now One Mile at a Time post: Iberia flights are starting to be loaded as awards that can be searched and booked on aa.com . Often when searching awards there, most of the availability is on British Airways, which has carrier-imposed surcharges that make it not worth considering for a "free" flight. Iberia's surcharges are modest, and this makes it easier to find transatlantic trips where AA miles are usable.