Chicago-Beijing-Thailand

Hello, we are planning a trip to Thailand in February, but would like to stop in PEK and try to take advantage of the 72 hour free visa. We plan on purchasing roundtrip tickets from Chicago to BJ, and separate roundtrip tickets from BJ to Bangkok. My question is, do we qualify for the visa if I show my confirmed ticket from BJ to Bangkok as my third country, and can we use another 72 hour free visa on our way back from Bangkok to BJ before heading home from BJ to Chicago?