We have generated a new type of biphoton state by cavity-enhanced down-conversion in a type-II phase-matched, periodically poled KTiOPO4 crystal. By introducing a weak intracavity birefringence, we obtained signal and idler photons whose quantum interference was modulated between singlet and triplet signatures according to their arrival-time difference. This cavity-enhanced biphoton source is spectrally bright, yielding a single-mode fiber-coupled coincidence rate of 0.7 pairs/s per mW of pump power per MHz of down-conversion bandwidth.