Elrond's family tree
(A table created from information given in The Silmarillion - opens in new window)
On his mother's side Elrond was descended from Thingol, Lord of the Sindar, and Melian the Maia. He was also of mortal descent, from the House of Bëor, the First House of the Edain. The Houses of the Edain were the tribes of men who first encountered the elves in Beleriand and remained their allies, fighting alongside them against the forces of Morgoth. The marriage of Lúthien, daughter of Thingol and Melian, with the mortal Beren was the first marriage between the Eldar and the Edain.
On his father's side Elrond was of Noldorin descent, and his line can be traced back to the Elven High Kings in Middle-earth through Turgon of Gondolin. On this side he was also descended from all three Houses of the Edain: the House of Bëor, the Haladin (the People of Haleth), and the House of Hador. The marriage of Tuor with Idril, daughter of Turgon, was the second marriage between the Eldar and the Edain.
Elrond and Elros are sometimes referred to as the Peredhil, or Half-elven. This acknowledges their mixed elven and mortal heritage. However, the mixture is not exactly 50/50. Their father, Eärendil, was literally 'half elven'. However, he married Elwing - also of mixed descent - and this is where the maths gets complicated. Elwing's grandmother, Lúthien, was 1/2 elven and 1/2 maia. She married Beren, a mortal, which makes their son Dior 1/2 human, 1/4 elven and 1/4 maia. Dior, Elwing's father, married an elf, which makes her 5/8 elven, 1/4 human, and 1/8 maia. Confused yet? When we get to Elrond and Elros, it's easiest to think in 16ths: from their father they have 4/16 elven and 4/16 human. From their mother they have 5/16 elven, 2/16 human and 1/16 maia. Put that all together and you get ... wait for it... 9/16 elven, 6/16 human and 1/16 maia. So they actually have more elven blood than anything else. But because even the smallest amount of mortal blood brings with it the 'gift of Ilúvatar', they have to make the choice between mortality and immortality, as do Elrond's children in whom the human blood is diluted even further.