Did Anthony and Gloria cheat on each other?

Anthony certainly cheats on Gloria. During the war, when he was stationed in South Carolina, he had an affair with a local girl by the name of Dorothy Raycroft. It's not hard to see why Anthony succumbs to temptation. Dorothy is just so incredibly real, certainly not the kind of woman he's used to meeting in his rarefied social world. And she's absolutely nothing like Gloria, the shallow, superficial, would-be movie star going crazy over the prospect of hitting thirty. Dorothy may not be as beautiful or as sophisticated as Gloria, but she has a wonderfully grounded air about her. In some ways, Anthony envies her. He's spent the whole of his pampered existence trying desperately to find a purpose in life. Yet here is someone with her feet firmly planted on terra firma.
Unlike Anthony, however, Gloria does at least grow as a character throughout the story. And crucially, she has a conscience. She abjures her youthful nihilism to embrace a weird religion called Bilphism. Whether it's due to her new-found spirituality or perhaps because she doesn't want to miss out on a share of Anthony's forthcoming inheritance, Gloria remains faithful to her husband. However ostensibly modern and sophisticated they may seem, Mr and Mrs. Patch are still in thrall to the prevailing double standards pertaining to relations between men and women.