In Chapter 14, at Port Stowe, the mariner tells Mr. Marvel about the story of the Invisible Man. This scene is an example of dramatic irony, since there is a large discrepancy between the mariner’s understanding of events and the reader's.
The mariner narrates to Mr. Marvel an extremely sensationalized story about the Invisible Man that he found in a newspaper. As he explains all the details of the story and speculates as to the whereabouts of the Invisible Man, Mr. Marvel gets more and more anxious—because the Invisible Man is standing right next to poor Marvel and whispering in his ear.
Of course, the mariner is blissfully ignorant of the real cause of Mr. Marvel’s anxiety, which makes the scene somewhat humorous. This exchange demonstrates the overall irony of the scene quite well:
"He didn’t have any pals—it don’t say he had any pals, does it?” asked Mr. Marvel, anxious.
“Ain’t one of a sort enough for you?” asked the mariner. “No, thank Heaven, as one might say, he didn’t.”
Mr. Marvel asks a self-interested question: he wants to know if the reporters are on to him—that is, if they figured out he is aiding the Invisible Man. The mariner replies conversationally and causally, starting with a joke, and then thanking that there is only one Invisible Man. The irony, of course, is that he is talking to someone who is in cahoots with the Invisible Man.
At the end of the chapter, after hearing the account of all the strange happenings in Port Stowe and Mr. Marvel’s connection to them, the mariner realizes exactly “how near he had been to the wonderful Invisible Man.” So, he is let in on the joke after it happened, and it all begins to make sense in retrospect.
In Chapter 21, Griffin tries to make his way through London with his new condition. One of the obstacles that he has to traverse is a crowd surrounding a band. The song that the band plays is the hymn "When shall we see His face?" Although the lyrics are not mentioned in the text, the hymn is well known and thus functions as an allusion. The song is about being able to see the face of God after death. Here is a sampling of the lyrics:
We shall meet to part no more, some bright golden morning,
At the gates of glory where our loved ones stand;
Songs of vict'ry fill the skies in that hour of greeting,
Endless days, endless praise, when we see His face.
The way this hymn functions in The Invisible Man is an example of dramatic irony. The band that is playing the music is unaware that an invisible man, whose face they can not see, is walking on the streets near them. Griffin and the reader are both aware of the irony.
The song's presence also strengthens the connection between Griffin and the Judeo-Christian God. These two entities, although they are very different in levels of benevolence, are similar in several respects. First, both God and Griffin are invisible, as mortals can see neither of them. Second, both have a great deal of power over human affairs, the Judeo-Christian God possessing omnipotence (i.e. infinite power) and Griffin having the ability to get away with crimes. Thirdly, skeptics deny the implausibility of both God and Griffin, insisting that empirical or science-based evidence is necessary to believe in them.