Aragorn is a Dunedain and Arwen is an Elf who has the power of immortality. Will their kids have the power of immortality ?
As one of Elrond's children, Arwen can choose whether to be an immortal elf, or mortal human. (IIRC there is a remark to this effect somewhere in the Silmarillion but I don't have it to hand.) She chose mortality, and that choice will affect her children as well.
The closest comparison is with Elrond's brother Elros, who became the first King of Numenor. He was a half-elf who chose mortality, and married (presumably) a mortal woman of Numenor. His descendants (including Aragorn, many generations later) were unusually strong, wise, and long-lived, but they were not immortal.
Aragon is descended from Elros, Elrond's twin brother, who being half-elven, chose mortality. This makes Aragorn a mortal man. On the other hand, Arwen is the daughter of Elrond, another half-elven, but who chose immortality instead. This makes Arwen an immortal elf. Therefore, their children will be of half-elven kind, and thus given the choice of whether they want
to be Elven and immortal, or to be of the race of Men and accept the Gift of Men which is death