First suggestion I'd make is to mix down your audio before exporting. Do both of the following, in this order:
- Sequence > Render All > Both
- Sequence > Render Only > Mixdown
Then save your project; then do your export.
Another possibility is that the voice track may be a different sampling rater/bit depth than your music tracks. Check the underlying audio files: are they 12 bit or 16 bit (aka 32KHz or 48KHz); are they mono or stereo. You can do this in FCE by selecting the file in the browser and doing Show Item Properties. Or open the files in QuickTime and view the Movie Inspector. What does it say for format (file type, sampling rate - should be either 32KHz, 44.1KHz or 48 KHz)?
What was the original source of the voice track? And are therre ANY effects on the voice clips?