Which airlines fly to Iceland. Would fly from Chicago to Stockholm. Next flight Bergen to Iceland. Return flight Iceland to Chicago. Any thoughts on how to do this much appreciated. Early summer timeframe.
Have you looked at Icelandair?
Based on a quick look any other airline has at least one stop/change on the KEF-ORD segment
Use the 'multi-city' search function
Icelandair has a free stopover program. I flew JFK-KEF then KEF-ARN. On the return you could fly BGO to ORD with a change of planes in Iceland.
All on Icelandair. Use the stopover button not the multicity option if you want to stay in Iceland.
The airport website lists all airlines that fly there plus the arrival times.
Also try a site like www.kayak.com to plug in Bergen to Iceland and it will give you options across multiple airlines.
From Scandinavia to Iceland your choices are SAS and Icelandair. But from Chicago to Stockholm and then Bergen to Chicago via Iceland, this sounds like an open jaw ticket with Icelandair with a stop over on the way back would be perfect for you.