So, keeping Gandolfini as Tony Soprano in mind as an example, here are some ways we fiction writers can make our characters more real--as opposed to, God help us, more likeable.
- Embrace contradiction. Tony was a wildly violent man who fretted over his violent tendencies, took his daughter to visit colleges, and became quite fond of a family of ducks. We all fret about certain characteristics we possess; we don't think they're quite honorable or consistent or helpful, yet we can't quite smooth ourselves out. Your characters can be the same way: an elementary school teacher who fears children, a doctor who's addicted to cocaine ... Let them be aware of these contradictions without knowing how to resolve them.
- Use interior monologue. The psychiatrist in The Sopranos was a device than enabled us to hear what went on inside Tony's head. In fiction, we can just write that stuff out. Where else but in fiction do we have direct access to another person's thoughts? Take advantage of that opportunity. After all, I think, therefore I am: that's how I know that I, at least, am real. Of course, you can overdo interior monologue or use it as an excuse to tell rather than show. The test is whether it reveals character, rather than explaining it.
- Let characters wonder what each other thinks. It's my sense (isn't it yours, too?) that we humans spend a lot of time wondering what other people think. It might be one reason why some of us read fiction--to at least have the sense that we're inside someone else's head. So a realistic fictional character would probably have this desire also--to know what her husband is really thinking about when he shrugs and says "nothing." Our common, everyday tragedy is that none of us can ever really know this for certain. In their world, your characters live this tragedy, too.
- Explore emotion. As Gandolfini said, let your characters really feel emotions. Those emotions can be confusing, "wrong," in conflict with one another, etc. They can explode volcanically, or the character can work hard at suppressing them, but the emotions themselves never go away.