I thought that I read on here (Fodor's) or maybe Trip Advisor that both the U-bahn and S-bahn are undergroud. Is that the case or was I just dreaming?

The S bahn goes below ground when it enters the city urban/downtown areas, otherwise it travels above ground.

Farther out in the suburbs the U-Bahn lines run above ground, too.

I am not sure what difference it makes.

Other than the general distinction of U-Bahn (subway) and S-Bahn (suburban) which in some cases can be blurred as pointed out, U-Bahn is run by MVG (Munich Transport Company, formerly the city council, which also runs buses and trams) and S-Bahn by Deutsche Bahn. There is an integrated ticketing system run by MVV (transport and tariff association).
It's similar to Paris's Metro and RER (run by SNCF, French National Railways), with integrated ticketing by RATP.

The difference is that I mentioned to my husband that they were both underground and he was ready to argue to the death that they are definitely not both underground. He has been there before and I haven't so he is right.

Thank you for your replies.

The difference between S- and U-bahns is only useful to folks with railpasses

railpasses are accepted on S-Bahns but not on U-Bahns

and weird but sometimes S-Bahns and U-Bahns can run on the same tracks.

S-Bahns are covered because as Alec says S-Bahns are run by the DB - German Rail.