In Christopher Nolan's Batman series (Batman Begins, The Dark Knight), family is incredibly important; the death of his parents is a driving motivation for Bruce Wayne to create Batman. However, Nolan constructs the father-son relationships as pinnacle, placing them as paramount to both Bruce Wayne and Jim Gordan.
Thomas Wayne-Bruce Wayne
In Batman Begins, there's a huge emphasis on the relationship between Thomas and Bruce Wayne. It is his father who rescues him from the cave, Thomas' business that Bruce inherits, and his father who he turns to in fear at the opera.
Martha Wayne is practically non-existent in the film; except for the scenes necessary to build up to her death (train to the opera, opera, in the alley), she's absent. I'm not even sure if they say her first name anywhere in the movie, but you can bet Thomas is mentioned by name.
Throughout the film, Bruce collapses "parents" with "father." Sure, Joe Chill killed both his parents, but the movie only establishes a relationship between Bruce and Thomas. Thomas and Bruce have conversations, while Martha's only line in the film is to scream when her husband is shot.
Indicatively, when someone wants to knowingly antagonize Bruce, they bring up his father. When Bruce confronts Carmine Falcone as a young man, Falcone intentionally demeans Thomas Wayne. Falcone says:
"Yeah, you got spirit, kid. I'll give you that. More than your old man, anyway. In the joint, Chill told me about the night he killed your parents. He said your father begged for mercy. Begged. Like a dog."Ra's al Ghul follows a similiar pattern, using Thomas Wayne as an access point to Bruce Wayne's anger. During a training exercise, Ra's says:
Your parent's deaths were not your fault. It was your father's. (Bruce attacks Ra's) Anger does not change the fact that your father failed to act.There's more references to Thomas thoughout the film (i.e. Rachel says Thomas would be disappointed in Bruce, or that Wayne Enterprises is going in a different direction than Thomas would have chosen, etc), but it's notable that while the death of both of Bruce's parents are used as character motivation, it is his father who recieves most of the attention in both Bruce's inner angst and external references.
Jim Gordon - James Gordon (son)
Here's another example of a father-son relationship highlighted while other familial relationships go ignored. In The Dark Knight, whenever we have a scene at Gordon's home, it involves him and his son. After Gordon comes out of hiding, his wife welcomes him home, however, he has a more moving scene with James.
The film establishes the father-son relationship as most important in a more explicit manner, though. When Harvey Dent kidnaps Gordon's family, he threatens to kill the person Gordon loves most, right in front of his eyes. As Dent moves his gun from Gordon's wife to daughter to son, Gordon yells out when Dent points the gun at James, causing Dent to assume Gordon loves his son more than his wife or daughter. Although James is eventually saved, his role at the end of the film re-establishes the prominence of father-son relationships to the Batman franchise.
What about mother-son, mother-daugther, or father-daughter relationships? Well frankly, there aren't very many to choose from.
There isn't much interaction between Martha and Bruce Wayne or Barbara and James Gordon. Until Gordon's whole family is held hostage by Harvey Dent, we don't see Gordon's daughter so there's virtually no father-daughter relationships at all. There are a few examples of mother-daughter relationships, however, they're very minimal and not generally as positive as the father-son connection.
In Batman Begins, Rachel's mother works at Wayne Manor and is present when Bruce falls in the bat cave and breaks his arm. As Thomas carries Bruce inside, she apologizes for any role her daughter may have played in the accident.
As for The Dark Knight, the only mother-daughter relationship exists between Det. Anna Ramirez and her hospitalized mother. In order to pay for hospital bills, Ramirez turns over police information to the mob. It's problematic enough to have one of the only WOC characters be corrupt, but it also casts a shadow over mother-daughter relationships in general because there's no evidence or examples of positive mother-daughter relationships.
So what does this mean? Well, it tells us that this Batman franchise is about men's relationships with other men. Not only are most of the characters in both films men, The Dark Knight is entirely about the trinity of Batman, Gordon and Harvey Dent. Rachel Dawes is an important character, but mostly because of the tensions that arise between her and Bruce and her and Dent. She is essential, but only because her death sent Dent on his crazy killing spree. The father-son relationships act to highlight this theme, underscoring the ways the films characterize masculinity. We are told/shown how to be a man, but not how to be a woman.
It'll be interesting to see how man-to-man relationships will be used in future Batman films, but also how woman-to-woman or woman-to-man relationships are missing, lacking, or purely sexualized.