Is it possible to mix split and single-supply circuit sections
Yes, it is, this is done all the time. The key is to make sure all supplies share the same ground. By sharing the the same ground the supplies current can find it's way back to the supply. 

One note: If you are passing DC from one circuit to the next, it becomes important to watch for voltage ranges. A ±5 supply that connects to the input stage of another analog section that has rails of 0V to 5V it might violate the voltage range of the input (most inputs have diodes that turn on after Vcc or Vdd plus the diode voltage usually 0.3V). For example an output of -5V going to an input that can't go lower than -0.3V might source too much current. In this case attenuators or series resistors might need to be added. 

In the case of capacitively connected audio, this would not be a problem. 

Here is an example of single ended and dual supply mixed:



All the voltage rails are generated with LDO's or DC to DC converters and share the same ground.