Personally, I think a sense of humor is more about being able to figure out if what a person says is really humorous or funny.
For example, I think the creators and writers of “South Park” have a great sense of humor. They approach their mocking of any belief, norm, topic etc. in exactly the same manner – to point out the ridiculousness in each, and to recognize that there’s an element of the ridiculous to them all, and finally to reveal whether that makes a practical difference or means an actual harm.
I think their approach to Mormonism is a particularly good example. When a Mormon kid moves to South Park, the family is portrayed as perfect and happy in a ridiculously extreme way. The willful ignorance they have regarding the rational analysis of their beliefs is made fun of in a telling of the story of Joseph Smith, portrayed as a clear con man. The disdain for the truth of it, from an objective perspective, is obvious.
However, in the end, the Mormon boy ends up giving a clear, irrefutable reason why Mormonism works for his family, that whether it’s true makes no difference if for them it produces love, and joy, and they make no attempts to convince someone to believe in it if they don’t want to – and tells Stan (the one questioning everything) to grow up and fuck off. It’s clear that in the end, the boy who’s Mormon is the hero – not because he’s Mormon, but because he approaches his beliefs with a mature attitude.
A person with a good sense of humor is able to pick out the ridiculous in us all and show it to us, so that we get the “Ah-ha!” moment along with the “Ha-ha!” moment (including, as said above, what’s ridiculous in ourselves).