Missouri is a pure no-fault divorce state so you don't have to prove your husband cheated before the court will grant you a divorce. The only available grounds is irretrievable breakdown of your marriage. However, the state does consider fault when deciding issues of spousal support, property division and custody. Therefore, your husband's adultery could potentially impact the final outcome of your divorce, but you'll have to work harder to bring it to the attention of a judge.
Gather the documents you'll need to file for divorce. In Missouri, these include a petition for dissolution of marriage, certificate of dissolution of marriage, statement of income and expenses, statement of property and debt and proposed separation agreement, and a filing information sheet. If you have children, you'll also need a parenting plan, which includes provisions and calculation tables for child support. All these forms are available from the court's website and they're unique to the state.
Complete the forms, paying particular attention to Box 50 in your petition. Although you’re limited to irretrievable breakdown grounds, this box asks you to explain if you have any allegations against your husband. Enter that he committed adultery so you have it on record with the court.
File your paperwork with the circuit court in the county where you reside. If you and your husband have separated, you can also file in the county where he lives. Ask the court clerk at the time you file about the best way to have your spouse served with your papers.
Gather acceptable proof of your husband's affair. You must get it through legal means. For example, you typically can't hack into his computer to find emails he and his paramour exchanged, but you can hire a private investigator to take photographs of them in romantic situations.
Attend a pretrial settlement conference when the court schedules it. This conference offers you another opportunity to bring your husband's adultery to the attention of the judge. The judge will ask if you and your husband are in agreement regarding all issues that must be resolved before you can be divorced. This is your chance to ask for spousal support, custody or additional marital property due to his behavior. Your husband will most likely object and the judge will schedule your matter for trial, where you can present the evidence you gathered.