One of the characters that Batman truly connects with is J'onn J'ozz, aka the Martian Manhunter.
The last survivor on Mars, J'onn came to Earth to help save it from invasion, and many times joins the Justice League afterwards.
For Batman, he sympathizes with the fact that J'onn is the last of his kind, as Batman is the last of Waynes, and thus he understands losing his whole world.
Batman also respects J'onn's vast powers, and often asks honest questions about it cause he expects certain things from him. At one point, he questioned why he didn't read someone's mind, as it should have been done to tell whether they were walking into a trap.
Many series depict a powerful respect between the two, and it's likely to continue in the comics and shows.