To show both Facebook Pages and Facebook Groups in one Social Stream module, you will need to create two channels in the backend (one for groups and one for pages). Then you'll be able to select both to display from within the SCSocialStream module. It should be as simple as that, but if you run into any difficulties with this working, please let me know.
By the way, when configuring the channel for a Facebook Page, the only pages that are displayed for the selected user are the ones for which the user is an admin.
-Melissa