It has been proposed that the charge exchange (CX) process at the interface between hot and cool interstellar gases could contribute significantly to the observed soft X-ray emission in star forming galaxies. We analyze the XMM-Newton/RGS spectrum of M82, using a newly developed CX model combined with a single-temperature thermal plasma to characterize the volume-filling hot gas. The CX process is largely responsible for not only the strongly enhanced forbidden lines of the K$alpha$ triplets of various He-like ions, but also good fractions of the Ly$alpha$ transitions of C VI (~87%), O VIII and N VII ($gtrsim$50%) as well. In total about a quarter of the X-ray flux in the RGS 6-30 AA band originates in the CX. We infer an ion incident rate of $3times10^{51},rm{s^{-1}}$ undergoing CX at the hot and cool gas interface, and an effective area of the interface as $sim2times10^{45},{rm cm^2}$ that is one order of magnitude larger than the cross section of the global biconic outflow. With the CX contribution accounted for, the best fit temperature of the hot gas is 0.6 keV, and the metal abundances are approximately solar. We further show that the same CX/thermal plasma model also gives an excellent description of the EPIC-pn spectrum of the outflow Cap, projected at 11.6 kpc away from the galactic disk of M82. This analysis demonstrates that the CX is potentially an important contributor to the X-ray emission from starburst galaxies and also an invaluable tool to probe the interface astrophysics.