Twins, even fraternal or non-identical ones, are usually thought to share the same parents. We know that's not true in cats, where members of a litter can often have different dads (female cats are nothing if not promiscuous when in heat). But people?
Yes, it's even true for people, although rare. Recently a couple of such cases have shown up in the media. One report describes a set of twins in Vietnam whose family thought they looked too different to really be twins. Well, they were right, since DNA testing revealed that the kids had the same mom (hard to fake that) but different fathers. And in Texas, it was also found that twin boys, born only seven minutes apart, were half-brothers, not twins, since they too had different fathers.
How does this happen? It's not as far-fetched as one might think — if fact there's a name for it— superfecundation. First, it's entirely possible that a woman might release two ova at a time — and if both get fertilized, voilà — fraternal twins, who might or might not be of the same sex. And, according to Dr. Keith Eddleman, (cited here) Director of Obstetrics at Mount Sinai Hospital, this is how superfecundation can happen: "A woman's egg has a life span of 12 to 48 hours, and a sperm is viable for seven to 10 days, so there's about a week's time for potential overlap and the fertilization of two eggs by two sperm from separate acts of sexual intercourse."
So the biology is clear — yes, there can be more than one egg released. And yes, sperm from two different men can fertilize one each — it's probably a matter of chance which one reaches the eggs first. What's not so clear is the situation surrounding these conceptions, and that we have to leave to each couple to sort out for themselves!
Thus it's not hard to understand why, for example, it's the mother's religion that determines a child's being Jewish or not — according to rabbinical law. Leaving aside modern inventions such as surrogate pregnancies and in vitro fertilization, you always know who the mother of a baby is. The father? Not so much.