This is quoted from epiuniverse.com, and it says it all. I don't see a picture on this thread, but here's a good description:

"It is most likely, that the plant you have, that you call "Night Blooming Cereus", is actually Epiphyllum oxypetalum. Oxypetalum is easily identified by its unique bloom. While the bud is forming, it grows pointing downward. A few days before it blooms, the bud starts to point upward. When it finally blooms, the tube resembles a "Dutchman's Pipe". This is also one of the names used for this plant. The flower is about 5- 8 inches in diameter, very white, and very fragrant. The bud opens around 10 PM and dies around 8 AM the following morning.

The growth is also unique. The stems start out either from an aureole of an existing stem or at the end of a long tubular growth that is very sturdy and can be as long as 4'. The stems are very flat, not thick, and have a slight wavy appearance to them. The aureoles are not symmetrical from one side of the stem to the other. They have a 'step' look to them in that an aureole on one side lies between two aureoles on the opposite site. It's hard to describe, but easy to recognize if you see it."

So, if this sounds like your epiphyllum, it probably is.