I think fay uses its own FFI, but with haste you just use the normal FFI to call normal javascript functions the same way you would interface with C code from haskell. There's no need for special bindings or anything. You could certainly make a wrapper for jquery if you were crazy (and I'm sure someone has already done so), but this idea that you need some special DOM library to do things that javascript already does out of the box is kinda odd.
Thanks for the clarification. The key part that I was missing was the FFI. I'd encountered projects like this in the past with either no FFI or no documentation for the FFI and I couldn't figure out how to talk to the DOM. I'm more than happy to drop down to javascript for those parts, but I wasn't sure that I'd have the option.