72 hour visa if arriving and departing from Kunming, but with layover in Beijing

Hi,

I will be arriving in China in Kunming and staying for 66 hours. I would like to apply for the 72 hour free transit at the Kunming airport. My return flight to the United States flies from Kunming, to Beijing (3 hour layover), then to Washington DC. Can I apply for the 72 hour free transit with this itinerary, or does the layover in Beijing (I won't be leaving the airport), mean that it is not available to me?

Thank you.