The best way to make a character believably complex is to come up with a detailed history for him. When you know what the character has gone through, it becomes much easier to answer "how would he react to this situation?" If you want him to be complex, make sure that a lot of different things have happened in his past.
Get to know your character well enough that you know what he would do. You'll know you're succeeding if you in a particular scene you want him to do A but realize that's not what he would actually do. From there, you can tweak the scene until he would actually do what you want him to do in that situation.
You've mentioned Asperger's and PTSD in particular. Research both of those and try to get a feeling for how they make a person feel in situations where they are triggered.
I haven't learned enough about PTSD to help you there. As for Asperger's:
Social situations are going to feel unnatural to him. He'll need to consciously think about body-language clues in order to really pick up on them. Some verbal constructions, like metaphors, will be harder for him to follow — he's likely to first interpret it literally. If he's young (<20) he's likely to not pick up on these at all. If he's older than that, he'll likely go quickly from realizing that a literal interpretation doesn't make sense to attempting to find the non-literal meaning. The first time or two he encounters a particular metaphor he's not likely to understand it on his own unless he has a chance to think about it for a while.
Along that lines, there are a lot of other things that he's likely to just "not get" unless he's had specifically read about it or been taught about it. Ballet is a good example — he'll be able to tell that what the dancers are doing must be difficult physically, but the dance will not evoke any feelings. It would be like watching a movie with beautiful music that really helps you connect to the characters and sets the mood, but with the sound off and subtitles on.
There will also be things that make him very uncomfortable. Perhaps it's movies where the characters are in an embarrassing situation, and he won't be able to separate himself mentally in order to be able to enjoy it. The overstimulation will be more than he can handle, so he will withdraw mentally and emotionally as a defensive mechanism. If you've ever had too much wasabi at once, I think it's kinda like that. That's why people on the autism spectrum will sometimes cover their faces or eyes or ears — they're overstimulated and need to do something, anything to try to cope with it.