That's right, you read correctly.
As it seem's, one of the biggest wishes Mark has for the big screen, is to see these two, meet face to face. Here's what he said to the The Huffington Post:
I am excited to keep coming back to this role. I see a lot of space for it to grow. I feel like there’s a lot of cool stuff to explore still, especially the relationship between Banner and Hulk. Hopefully, we’ll see the two of them in a scene together. That would be cool!
Even though they are the same, Hulk and Bruce, was actually a comic book where this happened. In The Incredible Hulk #315 of the original comic book series, Doc Samson, noting that Dr. Banner could make Hulk see hallucinations, came to the conclusion that Banner was a conscious entity inside Hulk, and decided to try and separate the two. Samson convinced the government to fund the experiment, and Hulk was placed into a nutrient bath while the procedure attempted to edit Banner out of the Hulk while leaving his intellect in a new body.