Two characters sharing a body is a rare but not entirely uncommon fictional phenomenon; alternating 'spoken' thoughts might also be needed for a character with dissociative identity disorder.
For the sake of avoiding spoilers
Unfortunately, if you're writing a purely fictional story, you can't rely on visual devices - which have also included different fonts and stylized word balloons in addition to the "two people in a control room" visual in the link above. Your tools are words, quotation marks, and italics.
Fortunately, making "internal dialogue" clear is not so hard to do, if you write and edit with an eye toward clarity. Let's have Bruce demonstrate.
If you're using first-person narration, it's pretty straightforward: Just punctuate the internal dialogue as dialogue.
The other guy was whining in my head. "This is stupid."
"I don't care if you think it's stupid," I thought back at him. "Betty wants to watch Bridesmaids. And so do I."
You can also do this in third-person:
"Puny sandwich," the Hulk spat in Bruce's mind, looking down at the thin bread and tiny slice of meat.
For once, Bruce had to agree.
The key is just to make sure that it's always clear who's speaking, just as in any dialogue. Fanfiction writers actually have something of an edge in this, as at least we usually don't have to re-introduce the initial concept.
You can also use italics to indicate internal dialogue, but that's more difficult to read.
Why do you use puny all the time anyway? Bruce thought at the Hulk-sized presence in his mind.
Dunno. Sounds right.
Bruce couldn't really argue with that, either.
In my experience, at least, it's easier just to treat internal dialogue as spoken dialogue and let your narration clarify where the thinking's happening.