Skip the mental math on connections for a moment and consider this: there is no nonstop option between Chicago and Malaga, which means the real decision on this route isn't which airline to fly, but which hub to route through — and that choice matters enormously for comfort. Business class from Chicago to Malaga almost always funnels through either Madrid on Iberia or London on British Airways, both of which operate under the transatlantic joint venture with American Airlines, so award availability and fare classes often overlap across all three carriers even when you're technically booked on a single ticket. I've flown both routings repeatedly, and my strong preference is via Madrid: Iberia's A330neo and A350 aircraft feature their newer business class with direct aisle access and proper lie-flat seats, giving you nearly the full ten-hour transatlantic stretch to sleep before a short regional hop down to the Costa del Sol.
That final MAD-AGP segment is where expectations need adjusting — Iberia operates it with recliner-style regional seating, not lie-flat, so treat it as a quick connector rather than a continuation of luxury, and budget at least 90 minutes in Madrid's T4S to clear the Schengen transfer smoothly, since Iberia's own lounge there is a genuinely excellent place to shower and reset before the last leg. The London routing via British Airways works too, and if you land an A350 or 777-300ER with the Club Suite featuring the sliding door, it's a strong alternative, but Heathrow's T5 connections to AGP are frequently on narrowbody aircraft with Euro Business recliners, so you lose the flatbed advantage on that final stretch either way.
Shoulder season — April, May, September, and October — consistently delivers the best combination of fare value and pleasant Andalusian weather, avoiding both summer's heat and inflated peak pricing. Given how often award space and fares shift on this AA-IB-BA triangle, setting up automated fare alerts is genuinely the smartest way to catch a premium seat before it disappears.