They're probably best described as post metal, which draws inevitable comparisons to Isis. But since Isis are one of the best bands to have smashed eardrums in the last 15 years, that can hardly be seen as a bad thing. And whilst the comparisons are justified to a certain extent, TDOHM are no mere copyists, taking the post metal template and throwing in elements of sludge and shoegaze.
Which I guess makes post-sludgegaze? Fuck, that sounds rubbish.
The Death Of Her Money play heavy music. They like big riffs, lots of distortion and a bit of shouting. They are very, very good and you need them in your life.