Bought round trip to Beijing and will buy round trip to Tokyo separately, different airlines

Hi,

I bought a round trip ticket from NYC to Beijing from Feb. 21-March 4, arriving at PEK on Feb. 22. I am then going to buy a round trip ticket to Tokyo but haven't yet, most likely on a different airline from Feb. 24 to March 4. So I will be spending a total of 2 days in Beijing and then on my departure, it should be a short layover that I plan on spending inside the airport. Does the visa-free travel still apply if I am using different airlines and if I bought all my tickets separately and am using different airlines? What are the things I should do to ensure that the visa-free travel is granted?