You really could have asked this question on Shir Hashirim, for which the whole structure of the text revolves around expressing the relationship between the Jews and Hashem as a relationship between husband and wife.
While it is a good question, particularly here it is crucial to reiterate that whenever we describe G-d we are only describing how he interacts with us, and not Him proper, since Him proper cannot be described at all.
Also, it is clear from the onset this question cannot be addressed while asserting egalitarian agendas, so if that is something you find difficult you may be stuck. I would encourage you to open your mind, though, since it is pretty clear in every area of Jewish thought, including Halachick, historical, and philosophical, that egalitarianism is not a Jewish value.
What comes to mind is that in general the Maharal parallels Man and Woman with form and material, where material is a physical reality and form is a concept that finds its expression in a material. For example, in a wooden chair wood is the material while "chair" is the concept expressed in the wood. While of course this just begs the question, what does this have to do with Man and Woman?
In general it's observable that men are more interested in concepts while woman are more interested in things. (Of course neither of these are inherently good or bad, just strengths each gender possesses and can use as they wish.) That's why we find more men being musicians, mathematicians, scientists, etc, while woman gravitate more towards helping professions that emphasis personal interaction more and intellect less. Obviously there are exceptions, and there is nothing wrong with a female scientist or a male occupational therapist, just trends that reflect a deeper spiritual reality. This is also why while there is a place for women in Jewish learning, the emphasis, in concept and execution, has always been on men learning. The role of the woman is to bring these concepts down into the physical world, by building a home and nurturing an environment that engenders Jewish values.
So to, in the quintessential relationship between man and women, that of husband and wife, the husband has more of an affinity for grasping and articulating concepts, while the woman has more an affinity to bring this concept into reality.
The sexual relationship between man and woman parallels these roles as well, though this forum doesn't feel as appropriate to discuss this. In terms of the actual child baring this is pretty intuitive though. The mother is the one who actually "gives birth" in a physical sense, while the man's contribution in more conceptual, not perceptible at the time of birth. Additionally his contribution is from outside of the body that produces the baby, while the female provides the physical framework for the baby to develop.
In terms of our relationship with Hashem, Hashem provides the concept, the spiritual values and realities we are meant to connect to, while it is left to us to provide expressions for these ideas in this world.