On the page for the Classic card (lowest tier) I find this:
Free travel insurance abroad as a guarantee of quality assistance during your stay and the most extensive coverage every time you fly with Iberia or another Group company.
Check the features of this service at your Europ Assistance Espaņa Centre,
(+34) 91 514 99 30
Travel assistance services
Your Iberia Plus card covers the following expenses: medical bills in case of accident; emergency dentist bills; extended hotel stay in case of accident; the costs of a flying out a family member and their stay; return flight due to death of a family member; transmission of urgent messages; baggage search and localisation; dispatch of personal objects (not replacement); advance cash in case of emergency; advance bail; civil liability insurance; lost connecting flight.
Information and help service
Very useful information for Spain and abroad on your business or leisure trip in relation to: health, leisure, sports, travel and tourism. Also, possibility of booking hotels, restaurants and transport and using the flower, taxi, fax and telegram dispatch service.
http://www.iberia.com/es/iberiaplus/classic/
Can anyone give more details about this?