When a typical commercial airliner flies overhead, what is the actual noise we are hearing?
It depends on the type of operation:

Approach (close to airport):


Much aerodynamic broadband noise from the air-frame
Modern turbofan engines are less noisy than the air frame during approach. But engines emit most of the tonal components in the sound.
Depending on the type of aircraft and angle of descent the pilot might need to use air-brakes to reduce speed. That will cause turbulence and noise.
On some Airbuses you hear a typical high pitch annoying sound that is caused by air flowing across cavities under the wing (Fuel Over Pressure Protector to be exact, not from the engine).


Departure (close to airport):


Pretty much all the noise you hear comes from the engines, such as the buzzsaw noise generated when the tips of the fan blades reach supersonic speeds. Hot high speed gases causes turbulence and that creates low frequency noise, especially behind the aircraft. 


Overflight at 35.000-40.000 ft:


What you hear is low-frequency broad band noise that originates from turbulence behind the engines. All the high and medium frequencies are gone because the air between aircraft and ground absorbs much of the sound. The sound will also fluctuate due to differences in wind speed, humidity and temperature, along with the flight path and along the sound propagation path. 


Further reading / sources

1. Conference lecture by Prof. Dr. Ing. J. Delfs,
Head of Technical Acoustics, German Aerospace Center

2. ECAC doc 29 (Technical documentation)

3. An Overview of Aircraft Noise
Reduction Technologies