In Yosemite, Whenever we try to use the dictation feature in OSX it mutes other sounds and active only the build-in microfone. You need to set some hidden preferences to make this work. Open Terminal and enter the two commands below:
defaults write com.apple.SpeechRecognitionCore AllowAudioDucking -bool NO
defaults write com.apple.speech.recognition.AppleSpeechRecognition.prefs DictationIMAllowAudioDucking -bool NO
After doing this turn off dictation in Systems Preferences, wait a few seconds and then re-enable it. You should now be able to dictate while audio is playing. I’ve only tried this while using a headset/headphones, it’s probably not advisable without. :)
To restore your system to it’s virginal state, run these commands in Terminal and then restart dictation:
defaults delete com.apple.SpeechRecognitionCore AllowAudioDucking
defaults delete com.apple.speech.recognition.AppleSpeechRecognition.prefs DictationIMAllowAudioDucking