There are half-elves, and half-orcs, but there are no half-dwarfs. God knows everyone wants to fuck elves, and even orcs can have pillage-babies, and humans seem to have a habit of sticking their dick into anything and everything, so why not Dwarfs?
Because Tolkien. J.R.R. Tolkien is why.
In Tolkien's Lord of the Rings and The Silmarillion, the elves (and later, men) were created by CEO god Iluvatar, a god of light and love and tree-hugging who was basically a stand in for the Judeo-Christian God. The dwarfs were created by Aule, a middle-management god of crafting and mining. Elves and humans can interbreed because Iluvatar re-used the elfin source code when making men. Dwarfs were built on different hardware, so they can't run the same software for making babbies.
Elrond is half-elven on his mother's side. Aragorn is 1/16th or some smaller fraction elvish. Thorin Oakenshield is a dwarf made of dwarf and dwarf from the finest craftsdwarfship, and menaces with spikes of dwarf, and don't you forget it.
Which might be why dwarves eventually go extinct...
They don't count; they're sterile, exactly like mules.
Dwarfs are known for their endurance against poisons, magic and illnesses. This is actually caused by their very aggressive immunological system which attacks anything not-dwarf. Had your world have medicine advanced enough, you'd learn dwarfs cannot receive a blood or organ donation from any other race, and transfusing their blood (even a small amount) to non-dwarfs triggers very strong immune response in the recipient, most of the time turning into an auto-immune response within hours.
The identification gene is recessive, which means that unless both parents have it, the gene will be dormant in their child. If a female dwarf has intercourse with member of any other race, the egg is very quickly targeted by the immune system, and has no chance of settling. Having sex with a dwarf woman on her period ends in a rather nasty rash, though some charlatans advise such acts as a cure for certain enduring STD's (it doesn't work btw, the blood merely aggravates the skin).
A male dwarf impregnating an elf, human or orc woman might very well end with an impregnated egg, but around 2nd to 3rd week the fetus starts attacking it's host, which triggers an immune response from the mother, thus terminating the pregnancy. These don't even register as a pregnancy, just a brief pregnancy scare due to late period.
There have been attempts at nurturing such conceptions, by suppressing the mother's immune system during pregnancy, but all attempts ended prematurely when the mother invariably got ill from having a bombed-out immune system. Interestingly, the half-dwarf fetus always managed to shield itself from whatever infection threatened the mother's health. Attempts at exchanging the otherwise-healthy fetus to a womb of a surrogate mother woman in similar stage of pregnancy were attempted by a lich wizard, but any detailed data was lost in the inevitable looting and sacking by heroic adventurers.