Husband flying from Houston- via Taipei (pass through only) to Beijing for dogs and return

Hi, does my husband need a visa to fly from Houston, Texas USA by way of Taipei and then to BJ. He will stay for 2-3 days and then escort 5 dogs back to the USA by the reverse trip. He would like to see a few places in BJ (The Temple of Heaven, The Forbidden City, Tienanmen Square) if possible,
but we want to be certain than he doesn't do anything which is not permitted. Does this qualify for the 144 hour visa free trip? Thank you in advance for your reply.