How are Emilia and Desdemona alike?
Both Emelia and Desdemona are victims of public opinion. Emilia has her reputation destroyed when she is rumoured to have had a sexual relationship with Othello. Iago listens to the rumour and says that it doesn't matter whether she's actually done it or not--the rumour itself is enought to make him believe it is true. Desdemona similarily has her reputation destroyed. Othello believes her to have cheated because of rumour and innuendo, not because of anything that he actually sees Desdemona do. Part of Emilia's downfall is due to Iago's misogynistic prejudice against women. He thinks that all women, especially Venetian women, are little more than prostitutes. Therefore, it is easy for him to believe that Emilia has acted immorally. Desdemona also suffers due to Othello's preconceived notions about her. Othello thinks well of women in general, but not of Venetian women. He falls into the trap of thinking that because she is from Venice, she is probably also immoral and is therefore capable of doing all that he suspects her of.
Emilia and Desdemona are alike in several ways. Start with the basics: they are both married to military men, and men in the same organization. This means they are used to their men being away, to living with risk and fear, and, as in the play, to following them when needed.
Both are somewhat passive, and both are betrayed. Both are loyal. Both respect Othello. Both have their lives destroyed by Iago. If you listen to the rumors Iago repeats, both sleep with Othello.