We have investigated the branching ratios and angular distributions of photofragments resulting from the two-frequency multiphoton dissociation of HD{sup +} from initial bound level v{sub i}=0,J{sub i}=0 induced by linearly polarized parallel laser fields of equal intensity of 1 TW/cm{sup 2}. Both the laser frequencies {omega}{sub 1} and {omega}{sub 2} are below the dissociation threshold with {omega}{sub 1}<{omega}{sub 2}. We have used the time-independent close-coupling method. Molecular rotation has been taken into account with J=0-9 in each of the two electronic states GS and ES. The photon absorption channels (n{sub 1},n{sub 2}) with n{sub 1},n{sub 2}=0-3 have been included when n{sub 1} and n{sub 2} are the numbers of photons of frequencies {omega}{sub 1} and {omega}{sub 2} absorbed. We have neglected absorption channels when (net) four or more photons are involved. This necessitates the use of 120 channels. All radiative couplings including those due to the intrinsic dipole moments of HD{sup +} have been considered in a truncated length gauge form of interaction. In the presence of intermediate photon vibrational resonance with the GS (1,0) channel, dissociation takes place mainly through the ES (1,1) channel. But the channel ES (1,2) dominates for frequency {omega}{sub 2} not satisfying the resonance condition.more » For linear polarization, preferential photofragment ejection along the field polarization direction (i.e., {theta}=0 degree sign or 180 degree sign ) takes place. On resonance, the angular distribution shows prominent rings that are peaks on the photofragment distribution away from {theta}=0 degree sign . We have presented the photofragment angular distributions of HD{sup +} for different (open) photon channels within the framework of dressed state picture, vibrational trapping and the bond softening, adiabatic path, and the nonadiabatic transition mechanisms.« less