Do I qualify for the 72 hour Visa Free Transit?

I have a US passport and travelling from New York to Manila for 11 days ,then to Beijing for 3 days then back to Manila for 2 days before returning back to New York. Does this qualify for a 72 hour free transit in Beijing. I have been to the Chinese Consulate in New York but did not give me a definitive answer, instead, I was given a phone number in Beijing International airport which I called numerous time and unfortunately not in service. Can anyone help me with this dilemma ?