It is possible to generate the low-divergence ion bunches through the interaction of equally or slightly different counter-propagating laser pulses. In this paper, in the framework of plasma beat wave (PBW), we have numerically simulated the simultaneous acceleration of Carbon/Hydrogen ion beams. Using a two-dimensional particle-in-cell simulation, we have shown that in an HC plasma mixture with an optimal hydrogen ratio of 1:5, the laser reflectivity coefficient reduces up to about 4.6%. This condition may provide the acceleration of low-divergence H+ and C4+ ions beam. The cut-off energy for protons and C4+ ions are about 27 MeV and 410 MeV, respectively at nH=0.2 nC. The values increase by about 15.6% for protons and 21% for C4+ at nH=0.7 nC. In the presence of an axial magnetic field, the energy absorption arrives at its maximum at the values of Ωs/ωp=0.1, where Ωs and ωp are the gyro-frequency and plasma frequency, respectively. Here, the average kinetic energy of the accelerated ions raises by 17.9% and 7.3% for Carbon and proton ions, respectively. Compared to the magnetic field-free case, divergence angles were suppressed at approximately 24.2% and 20.3% for the Carbon ions and Hydrogen ions, respectively.