I can say that I think Jack exhibits some qualities and traits that are usually thought of as feminine. Many viewers have commented on the unalloyed masculinity they discern in both Ennis and Jack, but while I agree with this regarding Ennis, I see Jack's character as an integration of masculine and feminine qualities.
Jack is nurturing and tender. Note his application of his wet bandana to Ennis's wound after the bear attack. Also note the gentle and tender ministrations he offers Ennis in the second tent scene. We also see him being receptive to being penetrated, an act that many macho straight men view with disdain (regarding a man submitting to it, specifically), and which has traditionally (if narrow-mindedly) been seen as a largely feminine, submissive posture by the larger culture.
I should stress that I'm not arguing that nurturing and tenderness are inherently feminine and not masculine, merely that our traditional culture has made such a distinction. Jack shows a healthy integration of both masculinity and femininity in his persona, and as such, actually displays more wholeness from a psychological perspective than does Ennis.