The future of Jacksonville Jaguars head coach Mike Mularkey is still up in the air, and many have asked what the rules are for interviewing and hiring coaches who are currently employed by teams in the playoffs. Typically, teams will have to wait until the bye week or when a team is eliminated from the playoffs, but there is a a set of rules that teams have to go by.
January 6 - Assistant coaches under contract with playoff teams that have byes in "Wild Card" weekend can be interviewed for head coaching positions through the conclusion of the Wild Card games. Teams must ask for permission to interview.
January 13 - Assistant coaches under contract with playoff teams that won Wild Card games may be
interviewed for head coaching positions through the conclusion of Divisional Playoff games.
January 27 - Assistant coaches whose team is participating in the Super Bowl, that has previously
interviewed for another team's head coaching job may have a second interview with the same team no
later than the Sunday prior to the Super Bowl.
As far as I know, the same rules apply for front office positions on playoff teams.