This may not be exactly what you were looking for, but I have been listening to a podcast entitled "The History of Rome" which begins at the founding of Rome and ends (or will end, as it is ongoing, though it's over 160 episodes in so don't let that stop you) with the exile of the last Western Roman Emperor.

The podcast is very accessible and the narrator is enjoyable to listen to (good humor/not monotone). It has a very broad focus covering all range of topics from military to social to religious, and while it delves into some fairly deep historical topics it should be pretty easy for someone completely unfamiliar with the subject matter to enjoy due to the style in which it is presented (many amusing anecdotes/humorous delivery).

I personally enjoy podcasts, and this one in particular, as I can listen to them at times when I couldn't normally read but still want some mental stimulation. I'd definitely recommend at least giving the first few episodes a try as it really is, in my opinion, of very high quality, and even as a student and lover of ancient history I have learned a lot from listening to this.