Am I eligible if I have two separate itineraries?

Would I be eligible for the 144-Hour Visa Free Transit if I have two separate itineraries where the first is a roundtrip flight from DC to Shanghai (2/12/2019-2/26/2019) and the second itinerary is from Shanghai to Bangkok (2/17/2019-2/26/2019). My total time in Shanghai is way less than 144 hours but do I qualify since the destination I'm going to is on a separate itinerary? Can I show my second itinerary as proof that I’m transiting to another destination and Shanghai is just a transit city? Thanks.