The possibility and probability of natural transfer of viable microbes from Mars to Earth and Earth to Mars traveling in meteoroids during the first 0.5 Ga and the following 4 Ga are investigated, including: -radiation protection against the galactic cosmic ray nuclei and the solar rays; dose rates as a function of the meteorite's radial column mass (radius ร density), combined with dose rates generated by natural radioactivity within the meteorite; and survival curves for some bacterial species using NASA's HZETRN transport code -other factors affecting microbe survival: vacuum; central meteorite temperatures at launch, orbiting, and arrival; pressure and acceleration at launch; spontaneous DNA decay; metal ion migration -mean sizes and numbers of unshocked meteorites ejected and percentage falling on Earth, using current semiempirical results -viable flight times for the microbe species Bacillus subtilis and Deinococcus radiodurans R1 -the approximate fraction of microbes (with properties like the two species studied) viably arriving on Earth out of those ejected from Mars during the period 4 Ga BP to the present time, and during the 700 Ma from 4.5 to 3.8 Ga. Similarly, from Earth to Mars.