Yes, It is possible to stream the videos within the members area of your membership.
Basically, what you'll need to do is use a third party solution for embedding of video such as:
http://transparentplayer.com - this is integrated to work with Nanacast's Amazon file hosting and security for source file securing. There is Nanacast use instructions inside the members area of that product. You host all files remotely on that one.
http://ezs3.com - They give you remote embedding code that you can paste into your HTML of your episode to display an embedded video.
The instructions for embedding video can vary per player, so the documentation/instructions for whichever player you choose is the best source to look for help on that topic.
Keywords: Video format, transparent player, mov, FLV, Mpeg