Friends with his ex??

Ladies i am so very depressed. I'm in love with a man that I've been with for 2 years. Last year during a time that i thought we were happy, he cheated on me with his ex of 11 years. Thinking it was over, i asked him why did he do it. Of course his response was it was an accident. He was just really drunk. In love, i decided to tell him to never do it again and to cut ties with her. Well over the course of 6 months now, they have not stopped talking! She says that nothing is going on and so does he. I disapprove strongly of this so called friendship but he won't stop contacting her. He wants me to trust him but he hides his phone and deletes his texts to her. Angry i confronted both of them and they both said again that nothing is going on. I have broken up with him about 6 times because of this and have gotten back with him only to find out he's still in contact. We went from arguing about it to fighting. He says that it's apart of his customs because he's from Nicaragua. He says that once you end the relationship nothing is wrong with them becoming friends... I asked him how would he feel if i did this to him? He said that he would murder me. He slapped me when his friend flirted with ME! i love him but I'm hurt to the core. I hate to give up my relationship but i feel like he just don't get it! How would each of you handle this??? I also thought about getting revenge and cheating on him. I didn't do it though. Help me please! I feel so lost...