Using the technique of quantum transport of the interfering pair we examine the Hanbury-Brown-Twiss (HBT) interferometry signatures for the particle-emitting sources of pions and kaons produced in heavy ion collisions at 10-30 AGeV. The evolution of the sources is described by relativistic hydrodynamics with the first-order phase transition from quark-gluon plasma (QGP) to hadronic matter. We use quantum probability amplitudes in a path-integral formalism to calculate the two-particle correlation functions, where the effects of particle decay and multiple scattering are taken into consideration. Our model-calculated results indicate that both the HBT radii of pions and kaons increase with the system initial energy density. The HBT lifetimes of the pion and kaon sources increase significantly when the initial energy density is tuned to the phase boundary between the QGP and mixed phase. This increase of HBT lifetimes will likely appear in heavy ion collisions with an incident energy between 10-30 AGeV.