You can't run AVAudioPlayer and the iPod player or MPMusicPlayer or MPMoviePlayer at the same time, without doing a bit more work. If you want easy, then use Audio Toolbox's System Sounds.
If you want to do some extra work, then you should look at Audio Sessions:
kAudioSessionCategory_UserInterfaceSoundEffects
For sound effects such as touch
feedback, explosions, and so on.
Equivalent to the
kAudioSessionCategory_AmbientSound
category, which you should use
instead. The
kAudioSessionCategory_UserInterfaceSoundEffects
category is deprecated in iPhone OS
3.0.
kAudioSessionCategory_AmbientSound
For
long-duration sounds such as rain, car
engine noise, and so on. It is also
for “play along” style applications,
such a virtual piano that a user plays
over iPod audio.
When you use this category, audio from
built-in applications, such as the
iPod, mixes with your audio. Your
audio is silenced when the Ring/Silent
switch is set to silent or when the
screen locks.