Was Adam created as complete man containing both male and female?

   Heb 1:3 Who being the brightness of [his] glory, and the express image of his person, and upholding all things by the word of his power, when he had by himself purged our sins, sat down on the right hand of the Majesty on high;

Since Jesus is the express image of God, and he is male, when that which is female was removed from Adam, it did not diminish what was originally in him. This is why , when Eve sinned, sin did not come into the world. Another Eve could be produced from Adam. But when Adam sinned, the full image of God was tainted.

Paul says that when he speaks of marriage (becoming one flesh) that he is speaking of Christ and the church. So Adam and Eve represent Christ and the church.

Christ is the express image of God, and the Church is made to be like him.

   1Jo 3:2 Beloved, now are we the sons of God, and it doth not yet appear what we shall be: but we know that, when he shall appear, we shall be like him; for we shall see him as he is.

In Genesis, God said he would make man in his image and likeness, then it only says he made them in his image. He does not complete making them in his likeness until Ge 5.1 after a lengthy narrative which has a hidden picture of Christ and the cross bringing forth a bride.

So it erroneous to presume that image and likeness are redundant terms. Christ, the man, is made in the express image of God. The woman, the church, is make to be like him.

Likeness is a subset of express image, and Christ possess both, but the bride only possess the likeness.

Lilith

Lilith appearing first as a demon within Jewish folklore (probably adopted from Sumerian sources) morphs into a human woman around 800-1000 AD in the Alphabet ben Sira. Medieval rabbis greatly developed the myth in the Zohar in an attempt to reconcile what they considered contradictory stories of creation. Since the Bible cannot contradict itself, they reasoned, there must have been two women created. The first, Lilith, was an equal to Adam, and the second taken from his side.

The alleged contradiction disappears when Genesis is properly divided by chapter between verse 2.5 and 6.

   4 ¶ These are the generations of the heavens and of the earth when they were created, in the day that the LORD God made the earth and the heavens,

   5 And every plant of the field before it was in the earth, and every herb of the field before it grew: for the LORD God had not caused it to rain upon the earth, and there was not a man to till the ground.

   6 But there went up a mist from the earth, and watered the whole face of the ground.

The word generations is towladah meaning record. It refers to the text preceding, not following as evidenced in pre-Babylonian tablets.

With the chapter division properly placed, it is evident that the second story does not contradict the order or creation, since the verbiage that would indicate a contradiction belongs in Chapter 1.

Verses 4 and 5 are a "closing parenthesis" on the first verses of Gen 1. Which is why the contents of the chapter is ignored. The heavens and the earth were created before the plants and man. It is a linguistic method for closing a chapter. Without the verbiage excluding plants and man, one might mistake the verses of Day 4 being the opening parenthesis. The next division repeats the subject matter of the last chapter by way of a hint: the water and the ground are mentioned in the last verse of the end, and in the first verse of the next chapter.

The way in which the creation story is being referenced is different, therefore there is no contradiction, and no reason to invent a second wife for Adam.

On authority

   Mt 10.4 And he answered and said unto them, Have ye not read, that he which made them at the beginning made them male and female, 5 And said, For this cause shall a man leave father and mother, and shall cleave to his wife: and they twain shall be one flesh?

Jesus taught that there was one man and one woman who became one flesh. Not one man and two women. The rabbis did not have the benefit of this teaching when they invented Lilith.

Two stories

When there are two things, one is a heavenly and one is an earthly representation of the same thing.

Genesis 1 is the heavenly view of creation, as viewed by God. Gen 2ff is the view from Adam's perspective. The way that creation is viewed is different. There is no contradiction.

Genetically

   Ge 2:21 ¶ And the LORD God caused a deep sleep to fall upon Adam, and he slept: and he took one of his ribs, and closed up the flesh instead thereof;

The word for rib also means side. Genetically, the human male has the XY chromosome pair, where the woman has XX. The woman was produced by taking one side of the male. The primitive rendition of Gen 2.21 is scientifically and theologically accurate. The male remained male, while the female was made to be something else (and how!) in his likeness.

Conclusion

Since Adam lost nothing when Eve was taken from his side, then he was male in the same way that men today are male, and there is no reason to presume that his genitalia was any different from men today.