How far can an airline's headlights be seen?

Airplanes turn on their landing lights below 10,000 ft.

Something at 10,000 ft could be seen on a clear night from as far away as 100 miles - up to 122 miles if there is nothing obstructing the horizon and the air was clear.

You can't get a really quantitative answer to this as there are various conditions at play.

For one, you can never have total clarity as the plane is usually high enough in the atmosphere that cloud formations interfere. Another is if you are able to [theoretically] look head-on at the lights or not. I'm assuming you mean at night....

These kinds of things affect the nature of the answer to your question, but under ideal conditions I can only guess at the moment, but probably several miles or more.

I see them routinely more than 40 miles away. Looking head-on, their movement is imperceptible, and they are easily confused with stars and fixed lights.