Some might argue that Webster is creating a dichotomy with the two women as the Duchess is noble, keeps her feelings to herself, and plays the roles that a woman should by being proper and following the will of the men around her for the most part. Julia, on the other hand, acts independently and tries to use her power as a woman to seduce Bosola and eventually pays for her dishonesty by kissing the poisoned book the Cardinal offers her.
In portraying the Duchess as the wonderful woman who is beloved by all around her for being so honest and virtuous and then juxtaposing that woman with Julia who is reviled and eventually killed because of her dishonesty and far more independent and devious nature, Webster does create a commentary about how a woman ought to behave with clear guidelines and rewards for the one who does behave properly.
Yet there are things about both women that suggest that Webster is not against a woman being independent. The fact that the Duchess chooses to marry someone that is lower than her social and political standing suggests that she is not entirely bound by custom. This is mirrored by the willingness of Julia to use her powers of persuasion and her sexuality to try and get what she wants suggesting that some level of independence is acceptable and perhaps even celebrated.