Of Antisthenes' rather prolific writings, the only non-fragmentary works that have survived are the Ajax and the Odysseus, both of which are rhetorical, not philosophical. His fragments tell us very little of the sort of thing that you're asking, and indeed there's extremely little evidence to base any argument on Antisthenes' views on women in any of our texts at all. However, both Xenophon and Diogenes Laertius mention Antisthenes speaking of women and the relationship between women and men rather briefly. Antisthenes appears as a participant in one of Xenophon's Socratic dialogues, in which he mentions that he thinks that just as virtue is shown by action, not by opinion, marrying a beautiful woman and begetting children on her is a wise and virtuous thing. Diogenes Laertius mentions women more prominently. According to Diogenes Laertius, Antisthenes used sex as an example of one of the pleasures that he thought a virtuous and wise man should abstain from. Diogenes quotes him as saying: "χρὴ τοιαύταις πλησιάζειν γυναιξὶν αἳ χάριν εἴσονται," (let us make love to the sort of women who know grace). What exactly that means I can't really say--I'm no philosopher. Most commentaries I've seen indicate that χάριν there is supposed to mean "thanks," which is how the word is pretty regularly used, but it doesn't necessarily mean that, it could have a number of different meanings all encompassed by the English word "grace" (personally I don't understand how the statement makes sense, even in context, unless we use χάριν as it's meaning of "loveliness" or perhaps its meaning as "delight," or "kindness"). Neither of those passages really tell us anything, but here's a kicker--Diogenes quotes Diocles as reporting that among Antisthenes' famous sayings was:

ἀνδρὸς καὶ γυναικὸς ἡ αὐτὴ ἀρετή

The virtue of men and women is the same

That's a pretty big deal right there. Although some philosophical schools appear to have had a high opinion of women, rarely do we find such a blunt statement. Since the crux of Antisthenes' philosophy was that virtue is the greatest good and we should all strive for virtue, then this statement implies that men and women have the same end goal and can reach it by the same means. The Cynics appear to have taken this a bit further. Diogenes shunned marriage, declaring it a civil institution that had not part in a wise man's life. But his pupil, Crates, took a different view, as he was married to Hipparchia. Crates and Hipparchia are among the more famous couples of antiquity, because their brand of Cynicism took on a very remarkable form. We don't have much evidence for them, and a lot is possibly slander (such as the reports that they would have sex in public, although that is somewhat in character for Crates' form of Cynicism), but it seems that not only were women accepted into the Cynical fold (as it seems that had been with Diogenes too), but to Crates women were equals with men. It appears to have heavily influenced their pupil, Zeno, who founded the Stoic school--Zeno writes that men and women are equal and should mix freely.