This is the case of "The Standard that Isn't".
November's 26th day in 2015 ... or ... The 26th day of November in 2015. They're both clumsy, and if one uses something clumsy long enough, it wears a path, and both sides are arguing from their well-worn paths. I've even heard of people refusing to use the number for the month -- month's aren't numbers. Instead of "26/10/2015" they might insist of "26-Nov-2015", or even "2015-Nov-26".
However, the latter has the advantage of being in order of magnitude. Days are sub-elements of months, and months in turn are sub-elements of years. But even that's just a preference for a style or purpose, consider "Four-score and seven years ago..." and "Four and twenty blackbirds..."