It has been long known that Drift-Cyclotron Loss-Cone (DCLC) and Double-Humped (DH) oscillations can be unstable in a mirror trap because of the presence of an empty loss cone in the distribution of hot ions and that the instability can be suppressed by the addition of a small amount of warm ions with isotropic distribution. Unfortunately, previous analyses have been limited almost exclusively to the case when the populations of both hot and warm ions consist of the same single isotope. In the present paper, we studied the stability of DCLC and DH modes in a multispecies plasma with two different isotopes of hydrogen confined in a mirror trap. We found that both DCLC and DH microinstabilities can be suppressed by the addition of warm ions with isotropic Maxwellian distribution provided that the concentrations of different isotopes in the warm ion population are proportional to those in the population of hot ions. We came to the conclusion that overlapping of the full set of cyclotron harmonics of hot ions by the set of cyclotron harmonics of the warm ion mixture is essential for effective suppressing of the instability of DCLC and DH modes.