You can't go on like this.
And you can't go on like this because if you split he'll go to her. Think about that, you're with a cheating man who doesn't tell you the truth, offer you explanations or reassure you. A man you knows you're in turmoil, but is happy for you to be there, because it suits him.
He's hardly a prize worth hanging onto, is he?
Find your self worth.
And yes, they can deny, deny, deny. My ex did this. It sent me crazy, knowing in my gut there was an OW. His coldness, his utter contempt for my wellbeing, his cruelty and detachment were heartbreaking. I very nearly had a breakdown due to all the stress. I filed for divorce, he still denied it. He went on holiday with her three weeks after I threw him out, she posted pics of him and her on FB, he came back, still denied it, said it was my warped imagination. Friends saw them out together, he still denied it. He told our kids he was living alone, he was living with her. Only post divorce, he told me that he had been seeing her for two years before we split. He didn't tell me, because he said 'he wanted to keep his options open!!'
So he had watched me suffer, drive myself mad, and stonewalled me. The wife of twenty years.
The day I threw him out, was the day I started to find myself again. I can't tell you how much happier I became.
Good luck