For Jude, Sue, and Arabella, the drama of their lives borders (and surpasses) soap opera drama-levels at times. These are emotional creatures, and when they let go, they really let go, as when Sue exclaims to Jude, after they decide not to get officially married after all: 'Then Jude, let us go without killing our dream!' (5.4.62). Marriage is "killing [their] dream?" Sue definitely has a flair for the dramatic.
But while the characters emotionally cry about killing dreams and the meaning of love and marriage and pain and regret, the narrator views things with a bit of ironic detachment. He's like a Victorian Jon Stewart minus the occasional potty humor. The narrator has the ability to step back and comment on the action at times. The narrator is not simply conveying information about the characters or stories. The narrator is finding spots to interject some humor and take some jabs along the way:
The purpose of the chronicler of moods and deeds does not require him to express his personal views upon the grave controversy above given. That the twain were happy—between their times of sadness—was indubitable. (5.5.1)
Here, the narrator tells us right out that it's not his job to "express his personal views" about, for example, the marriage plans (or lack thereof) of Sue and Jude. He's just there to report the facts, folks—with some jokes at their expense. While Sue and Jude maintain deep emotional investment with their plot lines, the narrator remains much more detached.