That is to say, how did these two groups, who each recognised themselves as racially superior, intend to co-exist had they won the war?
While you wait for more targeted answers, you might be interested in some threads from the FAQ section on the "Axis alliance and post-war plans":
In "How did the Nazis plan to end the war, by that I mean, was there an endgame of when to stop, or did they just plan to take over the world, if so, what were their plans to do so?", /u/ScipioAsina made a very relevant comment here - 158 comments (thread), over 8 months old.
This comment is in response to another user talking about Nazi Germany's plans, however the bottom half of it discusses a research paper published by a section of the Imperial Japanese government that called for joint Axis invasions of the United States in the future.
Why were the German's and Japanese allies in WW2? Was there any mutual benefit? - 3 comments, over 10 months old.
Despite its short length, the commenters here give summaries of tension between Imperial Japan and Nazi Germany as well Japan's domestic political struggles' effects on their alliance.
What was the motivation for Japan and Italy to declare an alliance with Germany? What were Hitler's plans for Italian and Japanese men after the war? - 16 comments, over 2 years old.
The commenters here talk about the mutual dislike for Communism and spheres of influence to be created in the post-war world.