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But, by far, the best way to deal with combat is to do something that the American media is really bad at--realism and consequence. This means that perhaps the police will come after them, or the victim's mother will. People will be afraid of them. It will be in the news. People will randomly (actually for revenge) try to kill the PC's. They will sometimes fight people who are very weak (i.e. average human) and kill them easily, and then have to deal with the consequences. There will be lots of innocent bystanders. Make the combats full of repercussions and people will be a bit less willing to jump into combat so easily.
2. Background Check. So now that you've given a different spin to combat, how do you bring in role-playing? It starts at character creation. I have a character bio sheet that I give all my players (mine is actually 4 pages long!). I tell them that by the second or third adventure, I want the bio filled in. The bio is full of all sorts of questions that leads the players to think a bit more in depth about their character. The bio includes things like: name, address, birthday, etc, but also things like-where did you grow up? How was your relationship to your parents? Talk about your relatives, your childhood. Where did you go to school? What are you afraid of? Who is the last person you'd like to run into and why? How do you feel about your career? Etc. After people spend an amount of time working on their bio, they tend to want to incorporate it. Reinforce this by bringing up things from each character's past every now and again.
3. Plot. Give them plots where they have to keep someone alive--someone they have to role-play with. Give a succession of situations where if they just kill people they don't the info they need to complete the mission. Have the plots deal with a variety of combat and non-combat issues.
4. Supporting Cast. Make interesting NPCs that the players will want to interact with. I find it most effective to make them random people. I don't know why, but the PCs I've encountered will role-play with the plain-looking secretary who is shy and flirty or the drunk 7-11 guy with a mohawk for a half hour. Populate the world with interesting people, who seem to have a story, the players will follow.