Is Emilia part of Iago's plot, or does she truly believe that Iago is saddened by what happened to Cassio?
As the other answer to this question says, Emilia is just as fooled by Iago's vile schemes as anyone else in the play. Though she plays a part in Iago's plotting, Emilia plays her part unwittingly, and it is not until the end that she realizes the villainy behind her husband's actions. As proof of this fact, take a look at Emilia's response when Othello informs her that her so-called "honest" husband told him about Desdemona's infidelity in Act 5, Scene 2:
If [Iago] say so, may his pernicious soul
Rot half a grain a day! He lies to the heart.
She was too fond of her most filthy bargain. (186-88)
These are clearly the words of a woman taken totally by surprise. Moreover, upon discovering her husband's treachery, Emilia rains verbal abuse down on Iago, thus illustrating the anguish she feels in discovering both Iago's true colors and the part she played in his machinations. With this idea in mind, it's safe to assume that, initially, she does believe that Iago is distraught over Cassio's downfall, and it is not until the end of the play that she realizes her error.
Iago completely dupes and manipulates Emilia. Emilia recognizes that Iago has an edge to him when he verbally jousts with Desdemona about womanhood and the relations between the sexes, but she is just out to satisfy her husband so she buys whatever Iago is selling. She would not suspect Iago as being the puppet master behind Cassio's falling out of favor with the Moor. Emilia is not part of Iago's plot, she just enters into the play at crucial moments and is just as surprised, shocked, and betrayed as everyone at the end of the play to learn of her husband's brutal manipulationsCheck out Emila's character analysis below for more evidence of her willingness to please her husband.