Scheduled to air on primetime TV Monday night are a pair of Apple (AAPL) iPhone advertisements that highlight one of the few things AT&T’s (T) network can do that Verizon’s (VZ) can’t: surf the Web in the middle of a phone conversation.

(AT&T’s GSM network allows simultaneous voice and data connections; Verizon’s CDMA network does not.)

The spots — posted below the fold — follow a series of high-profile Verizon ads attacking both AT&T and, by association, the iPhone, for the shortcomings of the carrier’s 3G network.

Apple’s response — showing users a feature that they may not have been aware of  — is considerably more subtle than AT&T’s, which accused Verizon of false advertising and sought relief from its ad campaign in the courts, so far without success.

The ads are scheduled to run during House, Dancing With the Stars, How I Met Your Mother, One Tree Hill, Big Bang Theory, CSI: Miami, The Daily Show, and the late-night talk shows (Conan, Kimmel, Fallon, Craig Ferguson).

Below the fold: the new ads.

[youtube=http://www.youtube.com/watch?v=V0TdgnYciGY]

[youtube=http://www.youtube.com/watch?v=PZ0Gx1qESmw]

See also:

• Verizon to AT&T: The truth hurts
• Verizon vs. AT&T: There’s a map for that

[Follow Philip Elmer-DeWitt on Twitter @philiped]