[Legolas]

Elves cannot give up their immortality.

It is simply not their choice. There are only three instances of Eldar (elf) and Edain (man) being wed.

This statement has its problems, in that we're only entirely certain that Luthien/Beren and Tuor/Idril fit.

1) Luthien was granted that choice because of what she and Beren accomplished with the Silmaril and all. A very special case. In this case, Luthien lost her immortality.

2) Tuor was granted the privelege of marrying Turgon's daugher, Idril. He was given the oppurtunity because of his interaction with Ulmo and what he accomplished. In this case, Tuor was granted immortality, and Idril remained as she was. Eru granted Tuor immortality...not Manwe, in that immortality wasn't his to give to men.

3?) Arwen and Aragorn obviously, though Arwen was half-elven. Elrond's parents had both elvish and human blood - Earendil with human blood from Tuor, Elwing with human blood from Beren.

From Appendix A of Return of the King:

But to the children of Elrond a choice was also appointed; to pass with him from the circles of the world; or if they remained, to become mortal and die in Middle Earth.

Thus, if Arwen's marraige was considered a marraige of Eldar/Edain, then it is possible that there were two more...Elladan and Elrohir, if they wed two human women.

Also, if Arwen's marraige is considered a marraige of Eldar/Edain, then the marraige of Dior and Nimrodel is in question because while Nimrodel was of the Eldar, Dior (son of Luthien and Beren) was half-elven.

There is an odd, fourth marraige where Mithrellas, an elf maid of Nimrodel, bore Imrazor the Numenorean a son, Galador (the Princes of Dol Amroth came from this child), and a daughter, Gilmith. This marraige is not included in the "three" because, she is a Silvan elf, i.e. not counted among the Eldar because she turned away from the movement west. We don't know if she died or not because " she slipped away by night and he[Imrazor] saw her no more" ("The History of Galadriel and Celeborn" - "Concerning Galadriel and Celeborn", Unfinished Tales).