It is important to keep in mind that the effectively universal opinion1 in Orthodox Judaism is that Gd takes no image. So when Gd is described as anthropomorphic in any Jewish literature, in order to understand that description, we must think in an abstract, metaphorical way.
This view is codified explicitly in Maimonides' 13 Principles of faith, which he outlines in his commentary on the mishnah ,(Sanh. 10:1). It is based on verses in the Bible, Deuteronomy 4:15, to name one. This stance is also evident from Tanaaic times, through Onkelos the Convert's translation of the bible into aramaic, where he goes out of his way to describe human-like attributes of Gd in conceptual ways, (one of many, many examples can be seen in Genesis 29:32).
Equally important is the concept of the oneness of Gd, discussed by Maimonides in the same place, and based on Deuteronomy 6:4. Maimonides puts it best:
"... not like one in a pair and not like one in a species and not like a single man that splits in to many individuals and not like one simple body that can be split up endlessly, rather He... is one in oneness, that there is none like it in oneness..."
So Gd having two literal images, or being of two genders, or having gender at all, or being two things contradicts fundamental Jewish belief.
All of that being said, we do see both genders relating to Gd. Generally, Gd is referred to as a male, whether He is referred to with the name Elokim, (Gen. 1:27), the ineffable name, (Gen 2:5), or the name of Adonut, (Gen. 18:30).
The only female word we find in relation to Gd is the Shechina, the dwelling or resting [of G-d's presence]. This name is alluded to in Ex. 25:8, and mentioned explicitly many times throughout rabbinic literature, for example by Onkelos in Gen 9:27, in Megillah 29a, or Bava Basra 58b. The Shechina is even referred to metaphorically as a niddah, a woman who is impure from her menses, in the extremely esoteric passage of קם רבי שמעון Which is from the Tikkunei Zohar, (see Artscroll Yom Kippur Machzor Hayim Yehezkel p. 56).
One way of understanding gender relating Gd is through the roles of men and women, seen most clearly and simply through the act of procreation. The male acts upon the female, who receives that action and nurtures it, creating new life.
Based on the above metaphor, one can easily see Gd as a male, for everything comes from Him, and He controls the world and acts upon it.
I have come across two understandings of the female role of the Shechina. The first is alluded to in Exodus 25:8, "And they shall make for Me a holy place, and I shall dwell amongst them". Notice that Gd dwells amongst us only after we make a holy place for Him. In order to have a realization and appreciation of Gd's presence in our lives and from our perspective we must preform an action which He responds to, cultivating it into a human realization of His Presence, as the female cultivates the actions of the male.
The second understanding is based on the final 'Heh' in the ineffable four letter Name, (I think I saw this in Jewish Meditation, written by Rabbi Aryeh Kaplan, z"l). Basically, the letters of the name describe Gd's conveying effects of His will from Himself unto us. The final Heh, the Shechinah represents His receiving His presence unto us, allowing us to be aware of and recognize Him. In accepting His presence from Himself unto us, His Shechina playing the role of the female in the metaphor, (Bear in mind the Oneness Principle).
1. I asked Rav Ahron Lopiansky about Corporealist Rishonim. He said that there are only two that we know of who even mention it as a possibility. One is the Ravad, who mentions corporealism as a mistake that some made. The other is Rav Moshe Taku, who discusses corporealism, but whose extant work is too fragmented to surmise any clear opinion or stance from. First and foremost it is a polemic against rationalism, esotericism, and any other processes of analysis that he felt "watered down" the simple meaning of the Bible and the Sages. Any mention of corporealism would then just be an argumentative counter claim to show the holes in such claims.
