Batman mostly fits the superhero archetype however does have some differences.
He has a weakness however unlike the normal superhero it’s not an object like superman as his cryptonite. His weakness is his morals on not killing people.
He has an alternate persona similar to spider man or iron man. However with Batman’s persona who chooses to wear dark clothing and not typical bright blue, red and gold that is often seen on superheros.
Last he makes a sacrifice and with all other superheros it messes with there morals. However unlike most superheros, Batman’s choice stops him from being seen as a hero.
Overall he does fit some of the superhero archetype however tends to change the way we see those elements. I would prefer to call him a tragic hero that has a superhero disguise over him than anything else. It is his own flaws that cause him to suffer.
The joker attacks and exposes Batman’s weaknesses. Every superhero has their own weakness. For instance, Superman has cryptonite which many villains use against him.
Joker causes Batman to deal with difficult moral situation. Choose Harvey dent or Rachel. This moral decision allows us as viewer to paint Batman in a new light.
They both have the same goal. They both have a version of Gotham that they want to have both of which are contradicting each other.
Batman becomes a better person due to Joker.
The joker creates his own material and doesn’t meet the normal cliche
Overall the Joker makes Batman better. It makes us (the audiance) understand Batman. We may see Batman as a hero or just a dick but either way we understand his reasons more because he doesn’t seem to be a powerful being. The Joker brings him down a peg and makes his character more human.