I run half-anything as an average of the bonuses/penalties of the two parents, whether this gives a +1 bonus or a -1 penalty makes no difference to me. Sometimes the numbers cancel each other out.
As to appearance, that's the player's prerogative. One of my past DMs allowed me to have a character that was fully Human, yet had glassy, jet-black skin. He was laboring under a curse.
If you want to get into the whole thing really deep, take anything that is genetic, like ability-score modifiers for race, and average the two sets as they stand, whether you are combining two totally different creatures or a half-breed and a member of one of its parents' races.
Anything cultural, such as stonecunning or the Elven training with swords and bows is discussed between DM and player, and the final ruling stands in future issues of the same culture.
Just as a guideline, I say that only certain races can breed with anything other than their own kind. Any creature with inherent magic, such as elves and dragons, can do so. Orcs have a very mixed-up genetic heritage, anyway, and so I allow them to crossbreed with any humanoid race, hence the half-orc. Dwarves can create the mul, from Darksun fame, with humans. In fact, humans are the only specie that uses magic that does not pass the ability through the blood.
There's more to it, long version, that I haven't, obviously, covered, but ya'll get the gist.
Steve