Iva is Miles Archer's wife, but she's having an affair with Spade, so we're guessing the marriage isn't exactly smooth sailing.
The narrator describes her as aging, but still beautiful. When we meet her in Chapter 3, she appears to be overly clingy with Spade and also pretty darn manipulative. Effie doesn't like Iva one bit and thinks that Iva had something to do with Miles's death. See, on the night of his death, Effie went to break the news to Iva, who pretended that she had been asleep the whole night. But Effie could see that the bed hadn't really been slept in and that Iva's clothes were still in plain view. Iva suspects Spade killed Miles, but of course Spade doesn't even bother denying her accusation.
We find out later from Sid Wise, Spade's lawyer, that Iva had in fact been out on the night of Miles's death. Miles had come home bragging to Iva that he was going on a date with another woman. Thinking that she could use this as ammo for a divorce, Iva followed Miles but instead of going to a restaurant, Miles was on the job tailing Thursby. Seeing that Miles had lied about the date, Iva simply went back home.
Iva comes off as the insecure, jealous type and even though Spade isn't really in love with her, he has to decide at the end of the novel whether to get back together with her.