Does it have to be a layover?

I have purchased two separate tickets. One two-way ticket from US-Beijing and a second two-way ticket from Beijing to HK. My plan is to stay in Beijing for 3 days and then go to Hong Kong for a few weeks. Then, I will take my return flight from HK-Beijjing and Beijing to US on the same day. Since I have purchased two separate tickets and this is not technically a layover, will I qualify for the 72 exemption? Thank you.