First things first, having a relationship with someone who is cheating on their spouse is playing with dynamite. Spouses always find out, and when they do, it's full of pain and turmoil, which you and your boyfriend will get dragged into. Condoms are not your only concern.
I'd be worried not only whether her husband is faithful, but whether your boyfriend is the only person she's having an affair with. She's proven herself to be a cheater and a liar, what reason could you have to trust that she's being honest anything?
You have every right to feel hurt and betrayed. You have every right to decide who you're sharing body fluids with, even if it's by proxy. You have the right to know they're not using condoms so that you can use them with him to protect yourself (which I recommend at this point).
STD tests are a minimum, but they don't guarantee safety. They don't catch things in the incubation stage, and they obviously don't protect against things you haven't caught yet.
Asking him to use condoms with her is not a big hardship. Yeah, yeah bareskin feels soooo good blah blah blah. Tough shit. She's having affairs, probably more than one, and that puts you at risk. But considering his reluctance towards honesty, you would be safer to use them yourself.
“As I am sure any cat owner will be able to tell you,
someone else putting you in a box is entirely different
from getting into a box yourself.” —bisexualbaker