The TVTropes article Fur Against Fang has this to say about vampires and werewolves in Middle-earth:
Werewolves despised vampires, considering them “rats with wings” and vampires regarded wolves like big bullies. It is not so evident in The Silmarillion, but when you read the Lay of Beren and Luthien and the meeting with Carcharoth, the text makes clear that Carcharoth is shocked of seeing a vampire and wolf together and wolves hate vampires.
On TVTropes, “Lay of Beren and Luthien” is linked to The History of Middle-earth. I assume that it’s talking about The Lay of Leithian in The Lays of Beleriand, but I can’t find the text “rats with wings” anywhere in that book.
Is there a passage that describes what werewolves and vampires thought of each other? I am looking for either the passage referenced on TVTropes, or anything else that describes what vampires and werewolves think of each other.