There's a story that often gets told that our system of Congress with two Houses, the Representatives and the Senate, are based on the Houses of the General Convention of the Episcopal Church, the Bishops and Delegates.
In trying to get to the heart of this tale, I sadly didn't find a lot of proof to support this claim. However, there is at least some historical consensus that ideas leading to this governance structure came from some of the same sources, particularly when it comes to John Locke. Locke's work was highly inspirational to the founding of America. For that reason, he is included in the St. John's College Great Books Program. In turn, William White, the 2nd Bishop of PECUSA (the Protestant Episcopal Church of the United States of America), studied Locke's teachings very closely too.
There also were many Episcopalians involved with the founding of America, and the first chaplain to the Constitutional Convention was an Episcopal rector. At the very least, then, there is an intersect between the creation of the Houses of General Convention and the Houses of Congress.
A lot of research steamed from my study of Church History under Dr. Ben King. If you are interested in learning more about the intersect of religion with American history, please read Jon Meacham's American Gospel.