The relegation-threatened Black Cats won the Premier League contest 2-1, ending Mourinho's 77-match unbeaten home league run with the Blues.
Mourinho could not hide his anger afterwards behind a sarcastic appraisal of the officials, while Faria was dismissed for angrily confronting the match officials.
Ramires avoided punishment at the time of his flailing arm striking Sebastian Larsson but now faces a retrospective punishment which could prematurely end his domestic season.
A FA statement read: "The FA has charged three members of Chelsea's staff following their fixture against Sunderland at Stamford Bridge on April 19, 2014.
"Chelsea midfielder Ramires has been charged by The FA for violent conduct following an off-the-ball incident that was not seen by the match officials but caught on video.
"Rui Faria, Chelsea's assistant manager, has been charged with two counts of misconduct.
"It is alleged that in the 83rd minute of the fixture, Faria used abusive and/or insulting words towards the fourth official (Phil Dowd). It also alleged that Faria's behaviour following the match referee's (Mike Dean) request that he leave the technical area amounted to improper conduct.
"Jose Mourinho has been charged with misconduct in respect of post-match comments he made following the fixture.
"It is alleged that Mourinho's comments constitute improper conduct, in that they call into question the integrity of the referee appointed to the above fixture and/or the integrity of Mr Mike Riley, general manager of the Professional Game Match Officials Limited, and/or the comments bring the game into disrepute."
A three-man panel of former elite referees reviewed the Ramires incident as it was not seen by match officials and "were unanimous that it was an act of violent conduct".
The Brazilian, who has been sent off twice this season, was playing only his second match following a three-match ban applied following his dismissal at Aston Villa, after which Mourinho was fined £8,000 for improper conduct for approaching match referee Chris Foy.
Ramires has until 6pm on Thursday evening to respond to the charge, while Mourinho and Faria have until 6pm next Monday to consider their responses.
Faria's case has been designated a "non-standard" one by the FA "due to the aggressive and/or threatening and/or serious nature of the reported behaviour."
It is the third time Mourinho has faced FA disciplinary action this term.
As well as the Villa Park incident which has left him seething, Mourinho was fined B£8,000 after accepting a charge following his dismissal against Cardiff in October.