"irreverent sense" means having a disrespectful or cheeky attitude towards something that is usually treated with respect or seriousness. Full definition
They have very different life experiences but similarly irreverent senses of humor. (mccooltravel.com)
We have very different life experiences but similarly irreverent senses of humor. (blondebrunettetravel.com)
I enjoy the company of an intelligent, self confident, adventurous woman who has a great, possibly irreverent sense of humor like mine. (loveawake.com)