I'm married and my husband and I are monogamous. As
briacon429 said, it's different for every couple, and even more so in the gay community. It sounds like you and your partner probably need to have a very clear talk about what is and is not within the boundaries of your relationship. For example, while neither my husband nor I are allowed to play with others, we allow each other to watch porn when we're apart. But talking/sexting with someone else would be a line to not be crossed.
My husband has crossed the line a couple of times over the 15 years we've been together. I've made the choice in each instance to stay with him in spite of those and it has been a tough process to forgive him. It takes time to gain that trust back and it definitely makes your home feel less stable.