No, Death in June is not a goth band, because they play Neofolk, Martial Industrial, while goth music consists of Gothic Rock and its derived genres, like Deathrock, Darkwave, Ethereal Wave, and Coldwave.

However, they do have a significant goth influence and even have some goth songs in their repertoire, like "Nothing Changes" and "All Alone in Her Nirvana".

If you want to dive into the goth music scene, some of the bands that might appeal to you if you enjoy Death in June are Bauhaus, Christian Death, and Diva Destruction.