As far as I know there isn't currently any support for authenticated http podcast feeds in Rhythmbox or any of its third party plugins, as also noted on the mailing lists.
A program that is specially designed for managing podcasts is
gpodder, which is available in the repositories. As I know from experience, what it says about its support for authenticated podcast feeds in the FAQ is accurate. You need to open the program and then
simply add your username and password into the URL when adding a channel. gPodder will automatically see the provided authentication data and use it to authenticate to the web server. The syntax is http://USERNAME:PASSWORD@example.org/files/feed.xml.
An example of the authentication process in
gpodder is below:
The authentication works best in the 3.x series as sometimes it would fail in the 2.x series if the 'user name consists of an email', but as 3.2 is the default version in Quantal you should be fine.