It's a few years after the end of the Civil War. Lt. Gullivar Jones of the Navy is wandering New York City when he's whisked to Mars via a magic carpet. He meets and falls in love with a crimson skinned princess and encounters a new type of Martian, the Tither people, who sort of resemble the tharks but are red. Then, Gullivar is transported to years later--and we learn that the princess is Dejah Thoris' mother. The Tithers kidnap John Carter's Princess so the two go to rescue her from a hidden, tropical valley.
However, Jones is again transported in time---to a future where he meets Dejah Carter and discovers that Earth has invaded Mars and brought war to the planet.
This is an interesting cross-over, though I was disappointed with the overall execution of the story.