Multilingual site with 1 language blog

I’m developing a tri-lingual website in the languages English, Danish and Swedish. All pages and the menu are translated into the 3 languages, but the blog exists only in English.

The problem:
When having either the Danish or Swedish menu active and clicking Blog, which is linking to the English blog page, the English blog is shown as wanted, but also the English menu is. The menu should stick to being what it was.
I have tried to point to a Danish/Swedish Blog page, but then I get a 404 error.
I know I could setup the blog as a separate WordPress installation, but I would like to have only one installation if possible.

My website is: http://allanrasmussen.com