There are two sides to every marriage. Maybe three, if a child is involved. Or make that four, in cases where a “consulting spiritualist” enters the picture.

Thanks to that arithmetic, Arthur Phillips’ remarkable new novel, Angelica, is four books wrapped into one.

It’s a tale of being haunted, taking some cues from Henry James’ The Turn of the Screw. It’s also a study of psychosexual struggle, in the manner of Arthur Schnitzler (the Viennese writer whose Traumnovelle was the basis for Stanley Kubrick’s Eyes Wide Shut). To a lesser but still lively degree, it’s a late-Victorian picaresque about actors-turned-mediums just trying to make a living. And ultimately it’s a profound meditation on the shortcomings of memory, especially memory’s unconscious capacity to invent the facts.

The novel’s ambiguities and hybrid essence are evident right from the start: “I suppose my prescribed busywork should begin as a ghost story, since that was surely Constance’s experience of these events.”

The “Constance” mentioned by the narrator (whose own identity remains a mystery until well past the book’s halfway point) is Constance Barton, wife of medical researcher Joseph Barton and mother of Angelica. Constance’s efforts to give her husband a child have triggered miscarriage after miscarriage, and she is, understandably, continually anxious about her one surviving child’s welfare.

She is also increasingly fearful of any conjugal attentions from Joseph, since her doctor has warned her another pregnancy might kill her. When Joseph suggests that Angelica, at age 4, might finally be moved from her parents’ bedroom into a separate nursery and might even start going to school, Constance dreads the worst: separation from her daughter and the resumption of sex in her marriage.

She also starts seeing the worst. For with Joseph’s every nighttime touch, no matter how casual, Angelica on the floor below signals a distress of her own. Constance, rushing to her side, soon starts catching glimpses of a protean, predatory presence—sometimes with Joseph’s face, sometimes with the faces of other men—hovering over her daughter “like an angel of death or ancient god of love.”

Enter Anne Montague, a former stage actress who now makes her living contacting the dead, calming angry ghosts and taking care of other occult business. She agrees Constance has a problem (“Your walls sing with the unseen”), but her exact thoughts on what that problem might be are kept under wraps until the book’s second section, where Phillips’ mystery-narrator delves more deeply into Anne’s background.

As for Joseph, he emerges more and more as the villain of the piece. His not-quite-English background (his name has been changed from the Italian “Bartone”), his hinted-at experiences as a soldier on distant colonial battlefields and the unsavory nature of his scientific research (no matter that it’s for the benefit of mankind) all make him a carnal, violent, alien creature in Constance’s eyes, and in the reader’s eyes as well ... until, in the book’s third section, we enter more intimately into Joseph’s world and start seeing the Barton marriage from another angle altogether.

At this point the novel becomes rich with artfully orchestrated “mirror moments,” in which a gesture or word that seemed threatening or unsavory from an earlier perspective appears entirely innocent or reasonable from another later viewpoint—and vice versa. These increasingly incompatible “realities” achieve beautifully dovetailed synthesis in the book’s final stretch. To say any more would be to give too much away.

Phillips, some readers will remember, is the author of Prague, a rueful, wry account of young Americans checking out post-Cold War Budapest (yes, the title is a bit of a prank). He’s also the writer of The Egyptologist, a hijinks-filled tale about a preposterous 1920s archaeologist that won over many reviewers, although it struck me as having more stunt than substance to it.

No such worries with Angelica. Here rigorous craft is in perfect balance with volatile content, resulting in a shapeshifting puzzle-novel with a harrowing soul to it.