Anthony lied about Therese having an affair, ending their marriage.
Anthony's conversation with John was the only time in the strip that Therese's affair was mentioned. Anthony and Therese's marriage ended instead when Therese found out that Anthony decided that their marriage was over and essentially proposed marriage to Elizabeth in the "going after". Anthony could not admit to the Pattersons the true story of his divorce, so he concocted this story intended to elicit sympathy for him, and to further vilify Therese.
While I find it reasonably plausible, it seems to me that the author doesn't quite know the Pattersons that well; it seems to me that Anthony could have simply said that Thérèse packed her bags and left him with Françoise because of her insane jealousy of Liz and been the subject of mawkish solicitude. It's not as if the only way that a relationship can collapse is that one partner is caught cheating or anything, right?