US - Beijing - Manila with more than 72 hours break in Beijing

Hello,

We will arrive in Beijing from Chicago at 8pm on July 1st, then to Manila on July 5th at 2am.

I booked for a hotel stay in downtown Beijing for July 1 - 5 because we didn't want to check out at 12am on July 4th, which is the checkout time for most hotels, but we plan to be at the airport in the evening and wait for out early morning flight.

Do I qualify for the 72-hour visa free entry or do I have to apply for a transit permit at our nearest Chinese consulate/embassy?