While a male chauvinist is defined as someone who believes that men are superior to women, what would be a word for a man who believe that men and women have defined roles, without implying the superiority of one or the other?
a male traditionalist.
a fuddy-duddy; old-fashioned person, an outdated conservative.
Until a more gender-based neologism comes along, the best single word remains "sexist."
I haven't found this boiled down into a word or expression anywhere else, so we may be in the realm of invention. How about calling such a person a role-divisionist, or gender-role divisionist, and his/her ideology gender-role divisionism? It's a useful question, because in some contexts, there may be an important distinction between role-divisionism and generic sexism or chauvinism. (I suggest this without in any way disagreeing with other responders who seem instinctively to sense that any attempt to generalize about what is appropriate for men vs women is bound to fall afoul of reality, to say nothing of justice).
In a religious context this view is called complementarianism:
Complementarianism is a theological view held by some in Christianity, Judaism, and Islam, that men and women have different but complementary roles and responsibilities in marriage, family life, religious leadership, and elsewhere.
An adherent of this view is called a complementarian.
The belief that there is an innate and characterizeable (sp?) difference between Males and Females is called "Essentialism". People who adhere to such ideology are called "Essentialists"; basically they believe that there are certain "innately male" and "innately female" characteristics which are different between Men and Women, and which exist independent of cultural and social conditioning- usually on a biological and / or psychological level.
There is much debate over whether or not this ideology is Sexist and reinforces Gender Stereotyping. The ideology on its own at face value, though, does not suggest that there is any superiority of the sexes based on these traits- only acknowledges that the differences exist. The level to which they exist, and the additional ideologies held by the idividual with this view, is what would make it sexist or not. So I don't believe that there is anything inherently wrong or sexist with believing in biological and psychological differences between the two binary sexes on its own.
The belief that Men and Women have assigned roles is called Gender Traditionalism. When someone actively and willingly attempts to embrace and participate in the role of their biological Gender they are often called Gender Traditionalists.
Like with Essentialism, there is a lot of debate as to whether or not this is Sexist, but there are several forms of it with differing ideologies: Chritian Traditionalism (Gender Traditionalism rooted in Biblical scripture and Christian belief), Modern Gender Traditionalism (an intersection of Gender Traditionalism with Gender Theory and Feminist Ideology), standard Gender Traditionalism (which believes these roles are the most optimal for the sexes to fulfill and that they are necessary for a well working society), and so on. Like with Essentialism, too, none of these are inherently Sexist and it depends on the other ideologies the person has.
Edit: Please note that Essentialism does not inherently have anything to do with Gender Roles.
Gender Traditionalism (or the belief in and adherence to the traditionally "masculine" and / or traditionally "feminine" roles, behaviors, and other expectations which are socially assigned to your biological Gender) is not the same as Essentialism (believing that there are innate differences between men and women on a biological and / or psychological (or other) level). They are two different ideologies; you may believe in Essentialism without also believing in TGR, and vice versa.