Do we need a visa for Beijing China PLEASE HELP!!!!!!!

Please help me!!!! Are we ok to not apply for a visa??? I have many flights booked through different airlines. First flight is USA to Tokyo from Tokyo to Beijing. We will stay for 55 hours and have a tour booked with hotel accommodations. We are not leaving the city during our stay. Then through another airline from Beijing to Chaing Mai. But during that flight there is a layover in Kunming China. During which we will not be leaving the airport. It's Only a One hour layover. We are staying in Thailand for 9 days then fly to Hong Kong for 4 Days and then back to USA, Where we reside. We don't need a visa for any other country except China and do not have one to any other country. But, do we qualify for the 72 hour free transit even with our layover and no any to a third country?? Sorry for so much detail but I just want to be absoutly sure!!!