What does Jonas's mother have that is higher than his father's in The Giver by Lois Lowry?

Jonas's mother has a more prestigious occupation than does his father.

Jonas's mother holds an important position in the Department of Justice, while Jonas's father is a Nurturer, a person who cares for the infants before they are assigned families or released.
The career of Jonas's mother certainly takes precedence over the father's position; moreover, she allows it to supersede her concern for her family as well, because she often seems preoccupied by her court cases. For example, in Chapter 1, during the evening session of talking about their feelings, the mother mentions her concerns about a repeat offender of the rules. She says that seeing him come before her again has caused her "frustration and anger," along with some guilt that she has had no influence over him. Also, she worries that he will again come before her a third time, which will call for sentencing him to be released.

When Jonas's father speaks, he sounds much more maternal than his wife as he expresses his interest in the infants that are under his care; further, he is concerned about a particular little baby boy that he calls Gabe because his assigned name is Gabriel for the Ceremony, if he makes it. Then, when Jonas says that he is worried about the upcoming Ceremony, the father prattles on about the last one and what he remembers, and so on.

In this new world in which Jonas lives, traditional roles are not always played by men and women. Indeed, there appears to be a role reversal in this society of the future, at least in Jonas's family.