You might be interested in some threads from the FAQ section on the "Axis alliance and post-war plans":

• 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.
• 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.
• 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.
• During WW2, were there any conflicts of interest between Nazi Germany and Finland regarding the future of St. Petersburg, Estonia and other occupied territories? - 4 comments, over 1 year old.
• A commenter pulls up a proposed map by a German government agency during the war of post-war borders with respect to Eastern Europe and Finland.

Italians and Germans fought in joint operations many times throughout ww2. In essentially every engagement in North Africa involving German forces, Italians were also deployed, most notably the 2nd Battle of Tobruk and El Alamein. Although its important to note that not every Italian engagement with the Allies involved Germans in support. There were many more Italians in Africa than Germans.

In Greece, Russia, the Mediterranean, and Italy, Germans and Italians often fought in joint operations together.

Russia is kind of an exception, however, because though the Italians were holding their own section of the Don, once Stalingrad became encircled, all Axis forces gathered for an attempted retrograde. So to put this into perspective, the battle of Nikolajewka was the final battle of breaking the encirclement, and it was conducted with Italian soldiers of the Tridentina Alpini division, supported by remaining German tanks

I believe the only time German and Japanese troops operated in the same battle was at a submarine base in Madagascar. I saw it in a documentary but don't recall the name, but confirmed it here: http://www.combinedfleet.com/Madagascar.htm