It actually varies, believe it or not. Most ride spiels are in Japanese like Jungle Cruise, Star Tours, Splash Mountain, etc. But then Big Band Beat (awesome show) at Tokyo DisneySea and just about every sign in both resorts are in English. The Magic Carpet Theatre show also freely offers a hand-held electronic device (like a PSP) that displays english subtitles for that show. The parades also feature both English and Japanese parts in their songs.
It's majority Japanese, but enough English so I never felt completely out of what was going on.
-- PMM