I only recall one Burton movie reference in Schumacher's movies and that was Chase's remark about Batman liking strong women in skin tight vinyl with a whip. I guess the inclusion of Pat Hingle and Michael Gough counts, too.
Maybe that was merely a nod to what Burton did previously but Schumacher's Batworld was an entirely new creation. It sure didn't seem like the same world.

t:
Let me get this straight... you won't be able to take killing off a mortal man seriously in these movies, but you will be able to take seriously the concept of a man dressed as a bat waging an infinite war on crime for the rest of eternity without getting caught or killed. Makes perfect sense.