Blues manager Mourinho faces punishment for comments made following the shock 2-1 defeat to Sunderland - his first home league defeat in 78 games at Stamford Bridge.
Assistant coach Faria was sent to the stands after berating the match officials following Sunderland's late winner.
Mourinho had to drag Faria away from fourth official Phil Dowd as the hosts' protests turned ugly in the closing stages.
Ramires is now facing a premature end to the season after being charged with violent conduct for appearing to strike Sebastian Larsson with a flailing arm to the face.
Referee Mike Dean took no action at the time, but FA disciplinary officials have reviewed the footage and he now faces retrospective punishment.
The midfielder has already been sent off twice this season, and he could receive a five-match ban if the latest charge is upheld.
An FA statement read: "The FA has charged three members of Chelsea's staff following their fixture against Sunderland at Stamford Bridge on April 19.
"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."
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.
Mourinho could not hide his anger after his 77-match unbeaten home run ended, launching into a sarcastic appraisal of the officials in his post-match press conference.
"I want to congratulate Mike Dean," the Blues boss said.
"I think his performance was unbelievable, and I think when referees they have unbelievable performances I think it's fair also that managers we give them this.
"So fantastic performance, he came here with one objective, the objective of making a fantastic performance and he did that.
"I think it's also fair, congratulations to Mike Riley, because he's the referees' boss, and what they are doing during the whole season is fantastic, especially in the last couple of months, especially in matches involving the teams that were in the title race, it's absolutely fantastic.
"And I also congratulate Mr Mike Riley, thank you."