From the original 1992-1994 series

A bit of realism-induced humor can be found in Archer's Superhero Origin from issue #0. He discovered that his parents, a pair of televangelists, were corrupt killers, fled from them when they tried to kill him and went to a Tibetan temple where he learned martial arts and armed combat. However, when he returned to the U.S. to take down his parents, it turns out that they were arrested shortly after he escaped because of their criminal activities.
In issue #4, Sect member Mahmud stops to say a prayer after he and his accomplices shatter a church window while chasing Archer and Armstrong:
Mahmud: Also, help me get the evil bastard whose name I cannot speak so can get out of this lunatic country right quick.

From the 2013 reboot series

Issue #2, when Archer lashes out at agents of the One Percent cult when he learns that his parents have sold him out:
Archer: Betrayers! False prophets! Liar liar pants on fire!
Issue #6: Kay McHenry, a corporate mouthpiece (and future Geomancer) is caught by agents of the One Percent cult who try to dispose of her by trapping her in a an old subway car that's dropped in the ocean to be part of a seawall protecting against rising sea levels:
Kay: Wait— rising oceans? Then it's real? Global warming is real?
[Beat Panel as the two cultists just stare at her]
Cultist 1: Of course global warming is real.
Cultist 2: What are you, a friggin' idiot?