Can “meantime” and “meanwhile” be used interchangeably?

That's interesting. I have no idea the "right" answer, but here's how I use it. I say "meanwhile" to refer to something "over there" or elsewhere, and "meantime" to refer to myself. So, "In the meantime, I'll be here doing this; meanwhile, you'll be over there doing that."

"meantime" and "meanwhile" have been used interchangeably as adverbs since the 16th century. If it's good enough for Shakespeare...

And at our more consider'd time well read,
Answer, and think upon this business.
Meantime we thank you for your well-took labour:
Go to your rest; at night we'll feast together:
Most welcome home!
Hamlet Act II, scene I

I would say that the usage of both is the same; they mean the same thing. However, just don't forget the form. Don't ever, ever say "in the meanwhile". Meanwhile (comma',') would do. But I like Natalie's post. Meanwhile really does seem more sensible to use when you talk about something away from what's initally talked about.

meanwhile, back at the ranch...

The error here is in attempting to learn proper English from television announcers. :-)

Both words have more than one definition and they overlap, but the two are not identical. Generally, meanwhile means at the same time, during, concurrently. Meantime usually means the intervening time, or until. In spite of this, they can often be used interchangeably and are listed as synonyms.

Examples:

I have an appointment at 3:00. In the meantime, I will read the paper (I will read the paper until my appointment).

Farmer Jones was milking the cows. Meanwhile, his fieldhand was plowing the fields (milking and plowing take place at the same time).

Usually (but not always), the above uses would not be interchangeable, especially the first. You don't often hear "in the meanwhile".

I would guess that meanwhile is not as commonly used as a noun (but not wrong). In spite of the original questioner's experience, I would also guess that meantime by itself, without a preceding "in the..." is not as common, but also not wrong.