144 hour Visa Free

Hi,

Hope someone will give me some help!

Planing a trip next year to Australia and China.

Leaving USA for Australia and back to USA via Beijing, China.

Flying on Qantas/American Air USA-Australia; China-USA legs.

And flying Air China Australia-China leg.

Am I eligible for the 144 hour free visa (planing to stay 4-5 days in Beijing)?

I’m an American passport holder. At QANTAS and American Air offices nobody knows anything about this free visa. Decided to fly on Air China from Sydney to Beijing on the hope they understand all of this...

Thanks for all the help,

H.