Through the similes he uses to describe his wife, the speaker draws some interesting contrasts between the beliefs the ancients had about death and the beliefs that contemporary Christians had. He starts with the earliest culture—Ancient Greece, and then moves on in time up to his affirmation of belief in heaven. The way that each belief-system replaces the one that came before it makes this poem into a bit of Christian salvation history in miniature, at least, according to our speaker.
Line 1: By calling his wife a saint right off the bat, the speaker immediately signals his belief that his wife has not really died, but lives on in Heaven.
Line 2: The speaker uses a simile comparing his wife to Alcestis, who was also brought back from the grave (as the speaker's wife has been in this vision). The word "grave" makes us think of dead bodies, of course, which is kind of a jarring association after he introduced the notion of mortality with his mention of the saint in line 1.
Line 4: The speaker says that Alcestis was "rescu'd from death by force" (4), alluding to the Greek myth of how Hercules rescued Alcestis from the underworld as a host gift for her husband. "By force" suggests that maybe Alcestis didn't actually want to be rescued, which creates a contrast between the way good Christians are rescued from death—that is, willingly and happily.
Lines 5-6: The speaker compares his wife to woman purified by a ritual bath after childbirth according to Hebrew Bible law, saying that this purification "saved" her. What's implied here is a comparison between
the salvation of the Hebrew Bible, which was all about following the
rules, and the speaker's version of Christian salvation, which is a gift
Lines 7-8: In yet another simile, the speaker's
wife is "such, as yet once more I hope to have / Full sight of her in
Heaven without restraint." With this line, the speaker strongly affirms
his belief in an afterlife. He does not just "hope" or "want" to see his
wife again; he "trusts" that he will. Now that's faith.