Even though Russia has most of the teams, when the league was making its big push 5 years ago or so they put a lot of emphasis on being multi national. Now there is a team in Finland for example.
At one point ESPN 3 was even showing some KHL games in the early morning. Don't think they do anymore though.
They were showing KHL games on Eleven Sports early in the season, and showed their playoffs last year. I haven't noticed that lately, but they have been showing Swedish league games.