This question no longer applies to current versions of Ubuntu.
See Problem with .deb packages on Ubuntu 16.04 for a similar problem affecting 16.04.
I'm running Ubuntu 11.10 and have some problems with Ubuntu software center and the installation of debian packages.
If I download for instance the debian from https://www.virtualbox.org/wiki/Linux_Downloads and try to install with Ubuntu software center I got the window opening but I can see only the GTK Spinner.
The problem exists also with the package of my applications http://www.giuspen.com/cherrytree/ and http://www.giuspen.com/x-tile/ which I create with dpkg-buildpackage,
The same packages are opened and installed properly with gdebi.
Best Answer
This is a comon problem with the software center. It seems not to like .deb packages it does not already have packages for and they chose to not install gdebi by default. You can get around this by installing gdebi yourself and using it, instead of software center, to install .deb packages.
For similar reasons you might choose to also install synaptic which is another package the chose to drop. Sorry Canonical, many of us are simply not Windows or Macintosh users and we don't like being treated like cattle.