What is the relationship between man and woman in 1984?

Men and women are not expected to have genuine relationships in 1984. All loyalty, passion, and devotion are to be aimed at the state. 
Winston's unsatisfying relationship with his estranged wife Katherine is typical of how men and women are expected to behave in the new totalitarian order. The two have almost nothing in common and no natural sympathy for each other. They are expected to—and do—have sex once a week in a joyless way, for the purpose of procreation. For Winston, it is akin to torture. Yet he knows to actually enter into a loving relationship with his wife would be a thought crime. As he thinks to himself:

Desire was thoughtcrime. Even to have awakened Katharine, if he could have achieved it, would have been like a seduction, although she was his wife.

The state considers a loving, sexually satisfying relationship between a man and a woman a threat. When Katherine leaves Winston, he feels no regret. His relationship with Julia, in which he comes to care for her more than the state, is a crime that must be punished.