Arduino mega2560 play an mp3 file while reading another file - audio

Question

My setup is built of Arduino Mega2560 with an Adafruit's Music Maker shield.
I am running their "player_simple" example and listen (by earphone) to an mp3 playing in the background.
That's work.
Once I try to read additional binary file from the same SD card, in parallel to listening to the music, I hear a white noise through the earphone.
Also, the reading of the binary file from the SD card - fails.
After resetting the Arduino couple of time (by pressing the rst button on the board), I am managing to hear the music but the reading of the binary file never happens.
Questions:
I wonder what I am doing wrong? (see the code below)
Is there an option to read the binary file from the SD card while playing a song (loaded on the same SD card) in the background?
Here is the relevant part of the code:
void setup{
if (! musicPlayer.begin()) { // initialize the music player
Serial.println(F("Couldn't find VS1053, do you have the right pins defined?"));
while (1);
}
Serial.println(F("VS1053 found"));
if (!SD.begin(CARDCS)) {
Serial.println(F("SD failed, or not present"));
while (1); // don't do anything more
}
// Set volume for left, right channels. lower numbers == louder volume!
musicPlayer.setVolume(20,20);
// If DREQ is on an interrupt pin (on uno, #2 or #3) we can do background
// audio playing
musicPlayer.useInterrupt(VS1053_FILEPLAYER_PIN_INT); // DREQ int
// Play another file in the background, REQUIRES interrupts!
musicPlayer.startPlayingFile("/e01.wav");
myFile = SD.open("S1F25.bin"); // open the binary file
Serial.print (" myfile.read() = ");
Serial.println (myFile.read());
}
void loop() {
volume_control();
if (musicPlayer.stopped()) {
Serial.println("Done playing music");
while (1) {
delay(10); // we're done! do nothing...
}
}
delay(100);
}
void volume_control(){
volume = volume + 1;
if (volume > 90){volume = 90;}
musicPlayer.setVolume(volume,volume);
}