Old school mashups - what were they called?

I was watching a couple of YouTube mash-ups and thought of interwoven songs on variety shows and Broadway musicals.
I found one or two using “mashup” and “Carol Burnett” and thought of “Lida Rose/Will I ever tell you” from Music Man and of course the counterpoint songs that Sondheim uses such as the opening song/medley “A Weekend in the Country”. I also seem to remember medleys where multiple songs were dovetailed.
Are there any terms for any of these “old school mashups”?
Do you have any favorites?

I can’t think of any examples and I don’t have an answer regarding what the interweaving of songs is called, but surely someone does! I’d like to know, too.

Here’s the one from Carol Burnett (actual mashup is in the middle)
http://youtu.be/enPEtFXh3nE

Carol and guest star Ken Berry mashup of “Sing” and “Put On a Happy Face”.

med·ley   [med-lee] Show IPA noun, plural med·leys, adjective
noun
1.
a mixture, especially of heterogeneous elements; hodgepodge; jumble.
2.
a piece of music combining tunes or passages from various sources: a medley of hit songs from Broadway shows.

Yup, medley.

I normally think of medley as a series of melodies segueing (sp?) from one to the next. Will the term also apply when two melodies are interwoven? Or alternate ?

In the Wiki article for “No Sugar Tonight/New Mother Nature”, Burton Cummings calls it “transwashing”. Maybe he just made that up, though.

When me and my friends did it in High School, we called it a “mix”, even though we were neither remixing the songs nor making a mixtape per se.

Counterpoint song. Irving Berlin was renowned for this: some of include “An Old Fashioned Wedding” from Annie Get Your Gun, “You’re Just in Love” from Call Me Madam, and “Play a Simple Melody.”

My favorite counterpoint is the Tonight quintet from West Side Story.

Thanks all, looks like counterpoint song/counterpoint duet does it:
(caution, tvtropes) http://tvtropes.org/pmwiki/pmwiki.php/Main/CounterpointDuet

this led me to “Amazing counterpoint duet: 21 year old Barbra Streisand sings “Happy Days Are Here Again” while Judy Garland blends in “Get Happy.””
http://youtu.be/oKl7K4v9AoU

Oh oh! I get to use a term I learned just last week (through this YouTube video)

Will “quodlibet” or “simultaneous quodlibet” work for you? The latter is pretty close to what we would call a mashup today.

Also, here’s a post on the Beatles’ "I’ve Got a Feeling that mentions some popular music quodlibets:

cool. Thanks for the new word. I was also reminded that some of the medleys segue from one song to the next with a common word or theme. I’ll keep an eye out for examples.