The charged pion production reactions d(gamma,pi⁺n), d(gamma,pi^-p), HD(gamma,pi⁺n)X were studied using linearly polarized gamma-rays with energies in the range from 260 MeV to 370 MeV at the Laser Electron Gamma Source (LEGS). A solid HD target was used in this experiment for the first time. The beam asymmetry data for the d(gamma,pi^-p) reaction significantly add to the previously available data. This gives new input to multipole analysis of pion production. A slight deviation from the beam asymmetry predicted for the free neutron is observed. The cross sections in the d(gamma,pi^-p) channel agree with previous measurements.