American Express Membership Rewards and Chase Ultimate Rewards are both 1:1 transfer partners of Iberia. You can also transfer points to and from British Airways or Aer Lingus since they are both owned by IAG, as long as both accounts have been open longer than ninety days.
Chase Iberia Credit Card
Application Link (Target: 100,000; Current: 100,000)
Annual Fee: $95
Earning: 3x on IAG Airlines (Iberia, British Airways, Aer Lingus, and LEVEL) and 1x everywhere else.
Benefits: $1,000 voucher for flights for two people when you spend $30,000 in a calendar year, 10% discount on Iberia flights at iberia.com/chase10, and no foreign transaction fees.