Hong Kong - Shanghai - Taipei, does the flight have to be on same airline?

Hi,
i need to travel to Taipei from Hong Kong but would like to go via Shanghai for 24 hours to meet a friend. if i book a single flight from HK to Shanghai on one airline and book a separate flight from shanghai to taipei within 24 hours, would this be eligible for the 72hrs or 24hrs free transit policy?
thanks,
Tom