In the past, it was considered of utmost importance that children have a same-gender parental figure as a role model, lest they grow up to be confused about themselves, their gender identity, and their role in society. Divorce was considered to be especially difficult on boys, who often grew up without the archetypal "father figure" and were therefore at a loss as to how they could be men. Some argued that such boys would grow up feminized, since they had only their mother for a role model.
Although some psychiatrists still cling to that model, society has largely moved on. We are constantly eradicating gender roles in society (with the obvious exception being that only women can bear children) and it is benefiting children of both sexes. It used to be "common knowledge" that only a woman could take on a nurturing role like that of an elementary school teacher or a nurse, but now it is quite common to see male kindergarten teachers and nurses. It wasn't too long ago that everyone would have laughed at the idea of a female scientist or accountant, but now the world is full of them.
In this world of very loosely defined gender roles, does a parent still have a special duty to his/her same sex child that is not present with the opposite-sex child? Is there any real need to model gender roles for our children anymore?
Children, when they are young and first start to realize that boys and girls are different physically, are quite concerned (even if it doesn't show) with being "normal" and behaving "properly." They do naturally look to the same-sex parent as a role model more often. Since this is the case, it is the responsibility of both parents to model that neither sex is inferior. Usually in a relationship, one person has a more forceful personality than the other, but both parents should be sure that their relationship does not look as though one parent is subservient, or the same-sex child will identify that trait with his/her gender. Part of helping children learn about gender roles is simply modeling through actions, not just words, that people of both sexes deserve respect and fair treatment.
That having been said, the most important gender-role modelling is showing your children how to treat the opposite sex. Children grow up considering their parents' relationship to be "normal" and unconsciously feel unsettled if any romantic relationships they form later in life differ too much from their parents'. Thus it is important that you respect your spouse, even during fights, and don't throw around gender-specific curse words that will get your children thinking that either men or women are naturally inferior.
By making sure to respect your partner, and showing your children that just because you stay at home with them, that doesn't mean women can't have good jobs, or just because Dad works all the time doesn't mean men can't stay home and enjoy taking care of their children, you will do a fine job of gender role-modeling for your children.