Camille Chatterjee took on this question a decade ago. She argues that male-female friendship isn't just possible; it's important:

Although women dig men's lighthearted attitude, most male-female friendships resemble women's emotionally involving friendships more than they do men's activity-oriented relationships, according to Kathy Werking, at Eastern Kentucky University and author of We're Just Good Friends. Her work has shown that the number one thing male and female friends do together is talk one-on-one. Other activities they prefer—like dining out and going for drives—simply facilitate that communication. In fact, Werking found, close male-female friends are extremely emotionally supportive if they continuously examine their feelings, opinions and ideas. "Males appreciate this because it tends not to be a part of their same-sex friendships," she said. "Females appreciate garnering the male perspective."