Do onward flights on separate tickets still count?

Would I (US citizen) and my husband (Swedish citizen) be eligible for 144-hr free transits if we fly on a round-trip ticket from Germany to Shanghai, but continue on from Shanghai after 3 or 4 days to Vietnam or Hong Kong on a separate flight itinerary? We will return to Shanghai from Hong Kong on the same day of our departure flight to Germany and not leave the airport between flights.

25 Dec - arrival in Shanghai from Germany
29 Dec - latest departure from Shanghai to either Vietnam or Hong Kong (we may leave on 27th or 28th)
4 Jan - return to Shanghai *airport only* for departure flight back to Germany

Thanks so much for any help!