The hadron-quark/gluon phase transition is studied in the two-phase model. As a further study of our previous work, both the isoscalar and isovector-vector interactions are included in the Polyakov loop modified Nambu-Jona-Lasinio model for the quark phase. The relevance of the exchange (Fock) terms is stressed and suitably accounted for. The calculation shows that the isovector-vector interaction delays the phase transition to higher densities and the range of the mixed phase correspondingly shrinks. Meanwhile, the asymmetry parameter of quark matter in the mixed phase decreases with the strengthening of this interaction channel. This leads to some possible observation signals being weakened, although still present. We show that these can be rather general effects of a repulsion in the quark phase due to the symmetry energy. This is also confirmed by a simpler calculation with the MIT-bag model. However, the asymmetry parameter of quark matter is slightly enhanced with the inclusion of the isoscalar-vector interaction, but the phase transition will be moved to higher densities. The largest uncertainty on the phase transition lies in the undetermined coupling constants of the vector interactions. In this respect, new data on the mixed phase obtained from heavy-ion collisions at intermediate energies appear very important.