IRVING, Texas -- Presiding over the worst defense in Dallas Cowboys history has earned Monte Kiffin a new job title.

Kiffin was named assistant head coach/defense on Tuesday night, while Rod Marinelli was promoted to defensive coordinator.

The Cowboys switched from the 3-4 to the 4-3 scheme with the hiring of Kiffin last year but finished last in the NFL in defense, allowed the most yards in franchise history and the second-most points in franchise history.

A master of the 4-3 scheme, the Cowboys hoped Kiffin could rekindle the magic he had for so long with the Tampa Bay Buccaneers as they moved from the 3-4. It never happened. The Cowboys hope Marinelli will have the same impact he had running the Chicago Bears' defense from 2010-12. The Bears forced the most fumbles (59), intercepted the third-most passes (65) and scored the most defensive touchdowns (13) in those three years while allowing the fourth-fewest points (904).

"Rod will be the defensive coordinator and have all the responsibilities that come with that. Monte's job transitioning us from a 3-4 defense to a 4-3 defense last year was a significant one. That will continue," Cowboys coach Jason Garrett said Tuesday night. "He'll do it from a little bit different role as someone overseeing the defense and working with Rod and the rest of the staff, coaching the coaches, coaching the players and viewing things from a different perspective. But we're lucky to have him. He knows this defensive scheme as well as anybody and his role will be significant.

"Rod will be in that defensive coordinator position and have all the responsibilities that coordinator job has and we're excited to have him in [that] role. He's been a defensive line coach, been a head coach, been a coordinator and we're excited to get him back in that role and have Kiff in the other role on the defensive staff. It can be good."

The Cowboys had injuries in 2013, losing players like Sean Lee, DeMarcus Ware, Morris Claiborne and Anthony Spencer for multiple games. They never had Jay Ratliff, who was cut in October. They also had subpar seasons from players they needed to play well, like Brandon Carr and Bruce Carter.

After the season-ending loss to the Philadelphia Eagles, Kiffin said he was not ready to retire and wanted to continue to be with the Cowboys. At the Senior Bowl last week owner and general manager Jerry Jones said Kiffin and Bill Callahan will return in 2014, but they will both be in different roles.

"He's going to be at every meeting, every practice, every game," Garrett said of Kiffin. "He's going to be completely involved in this and again viewing it from a little different perspective than he had last year. One of the things we're confident about is the fact that he and Rod work so well together. The roles will be a little bit different but having him coaching the coaches, coaching the players is a positive."

The Cowboys named Scott Linehan the passing game coordinator and will take over the play-calling duties from Callahan, who handled the job in 2013. Callahan will continue to hold the offensive coordinator/offensive line title.

According to a source, the Cleveland Browns were denied permission to speak with Callahan about a job on Mike Pettine's staff. A source told ESPNDallas that Callahan would not be pleased if Linehan would be added.