In the shard series, yes, drizzt did not have a defined background. That's why he wrote the trilogy after that, as he realized people liked Drizzt he needed to give him a story and depth. I guess it's the homeland series? Homeland exile and sojourn are the books I think. They do a decent job of setting up Drizzt as a surface dwelling drow.
The in born hatred of other elves just on the basis of them being surface elves didn't make sense to Drizzt, which led him to question pretty much every facet of dark elf culture.
When he spared the elf child, he rejected Lloth, which ultimately led him to Mielikki. Forget that Lloth took vengeance on his house, having his father sacrificed, for his actions.
From that point on there was no turning back for Drizzt.
Oddly enough, he still attempts to see the inherent good in all creatures, even orcs. For him to make the change makes him believe all those inherently "evil" beings can be salvaged.
Drizzt is nothing more than the mortal avatar of Mielikki really.
Though in a few of the later books, after he lost the companions, he devolved steadily into a far more wild version of himself, fighting more just for the thrill of the fight than for a purpose. Jarlaxle essentially has to save him from himself by reminding him why he matters. In my opinion Jarlaxle has also rejected Lloth and dark elf culture, though not as openly so as to avoid the reprisals he would face. And for him, it's more likely that drow life is simply too small and boring an ambition for him. Why rule a drow city when you can rule all the realms. I see him as a far more interesting character than Drizzt.
There was a real chance for Salvatore to move Drizzt to far more interesting places, but instead he regressed Drizzt back to what he was, probably for fear of alienating fans who want Drizzt to always be the hero. When faced with the tough moral questions, even in the worst situations, you know how he will act. That's what makes him so flat as a character.