Linux Mint Debian Edition is a rolling release distro based on Debian Testing. It is currently only available in 32bit and not for other architectures.
If you already have a Debian Testing installation, you will not have problems changing it to Linux Mint, if you wish to. This can be achieved by changing apt sources and preferences and installing Linux Mint meta packages.
Open /etc/apt/sources.list as root and append the following line at the end of the file:
deb http://packages.linuxmint.com/ debian main upstream import
If you want real Linux Mint Debian, you will need to remove other software sources like Unstable repos but have the following at least:
deb http://ftp.debian.org/debian testing main contrib non-free deb http://security.debian.org/ testing/updates main contrib non-free deb http://www.debian-multimedia.org testing main non-free
Now, open up /etc/apt/preferences and add the following:
Package: * Pin: release o=linuxmint Pin-Priority: 700 Package: * Pin: origin packages.linuxmint.com Pin-Priority: 700 Package: * Pin: release o=Debian Pin-Priority: 500
The above change will make sure that Linux Mint repos will be favored over Debian.
First upgrade your installation:
apt-get update apt-get upgrade
Now, install the following packages:
mint-meta-debian mint-wallpapers-extra mint-wallpapers-previous-releases
apt-get install mint-meta-debian mint-wallpapers-extra mint-wallpapers-previous-releases
If some installed packages conflict with the new packages, remove them and try again.
Now, change the default theme to Shiki-wise, remove upper panel and add notification area, mintmenu to lower panel and you are done.