The couple have been in a committed relationship for more than 20 years and have two adult children together, but Tweed told PostMedia that she has grown tired of Simmons flaunting his sexuality in public.
The season premiere of their reality series Gene Simmons Family Jewels culminated with Tweed leaving Simmons after seeing paparazzi images of the Kiss rocker posing suggestively with two young women. Simmons denied that anything improper took place, insisting that he had simply attended the same business function as the women.
Problems between the pair continued in June when Tweed stormed off an interview on The Joy Behar Show when Simmons attempted to make light of their struggles.
"He's a pig and I don't like it. I'm done," Tweed shouted as she left the show's stage.
Tweed has now described the two incidents as symptomatic of her and Simmons's disagreements, explaining: "I don't care about pictures, I care about real people. It's when things become real that it pisses me off. I wish someone had let me know it was an open relationship.
"If I'd have known, I'd have been doing the same thing, but he didn't let me in on the secret. That's what makes me the angriest."
Tweed went on to reveal that she is seriously considering ending the relationship unless Simmons agrees to change his behaviour.
"I've been trying for a long, long time. I hope for an epiphany, but good luck," the former model added.
Simmons recently described the state of his and Tweed's romance as "touch and go", lamenting that he is finding it hard to change his wild lifestyle.
> Gene Simmons: 'President Obama not qualified'
> Gene Simmons: 'Peace in Middle East possible'
Watch Shannon Tweed and Gene Simmons's argument during an interview with Joy Behar below: