dpkg supports installing packages for other non-native architectures using a system called multiarch. It was introduced in Ubuntu 11.04, so any later release should have it.
You can use dpkg --print-foreign-architectures command to find the added foreign architectures on multiarch e.g.:
% dpkg --print-foreign-architectures
i386
To find the native architecture, use dpkg --print-architecture e.g.:
% dpkg --print-architecture
amd64
Alternately, you can also read the file /var/lib/dpkg/arch to get a list of added architectures (first one is native, although you can remove it):
% cat /var/lib/dpkg/arch
amd64
i386