And I John saw the holy city, new Jerusalem, coming down from God out of heaven, prepared as a bride adorned for her husband. Revelation 21:2

And there came unto me one of the seven angels which had the seven vials full of the seven last plagues, and talked with me, saying, Come hither, I will shew thee the bride, the Lamb's wife. And he carried me away in the spirit to a great and high mountain, and shewed me that great city, the holy Jerusalem, descending out of heaven from God, Revelation 21:9-10

I will grant you that these two cities represent the opposing forces of good and evil, that of the Father and of Satan. I also agree that Jerusalem will eventually be the BRIDE of the King (the glorified Christ). But, nowhere do I find any relationship between "city" or "woman" with "church" or even "ekklesia". Both are called "city"s NOT churches. Would you describe the city where you live as a "church" or a "government"?

For unto us a child is born, unto us a son is given: and the government [not church] shall be upon his shoulder: and his name shall be called Wonderful, Counsellor, The mighty God, The everlasting Father, The Prince of Peace. Of the increase of his government and peace there shall be no end, upon the throne of David, and upon his kingdom, to order it, and to establish it with judgment and with justice from henceforth even for ever. The zeal of the Lord of hosts will perform this. Isaiah 9:6-7

We can better understand the concept of the New Jerusalem, City of God by looking at the Old Jerusalem.

Following is the first instance in the Bible that Jerusalem was more than geographical, where Jerusalem is treated as a separate person, along with a couple other examples.

Howbeit I will not rend away all the kingdom; but will give one tribe to thy son for David my servant's sake, and for Jerusalem's sake which I have chosen. 1 Kings 11:13

I have seen thine adulteries, and thy neighings, the lewdness of thy whoredom, and thine abominations on the hills in the fields. Woe unto thee, O Jerusalem! wilt thou not be made clean? when shall it once be? Jeremiah 13:27

O Jerusalem, Jerusalem, thou that killest the prophets, and stonest them which are sent unto thee, how often would I have gathered thy children together, even as a hen gathereth her chickens under her wings, and ye would not! Matthew 23:37

It appears that Jerusalem, both old and new (and Babylon) have been given (assigned?) separate corporate personality and are treated as entities separate from their inhabitants. Their attributes (sin or purity) and deads (killed the prophets) are then considered as corporate, not individual.

Jerusalem, the City (corporate, not the inhabitants), will become the bride. Christ, the King is in His Holy City, the Kingdom of Yahweh fighting a traitorous revolution waged by the enemy, Babylon, the City of Satan.