From an early age, Lia is made to feel suspicious of her body. She grows up in a vicarage, where the flesh that matters belongs to Christ. When she is 12, her parents, Anne and Peter, take in an adolescent boy, Matthew. Anne and Peter grow to love Matthew. So does Lia – but in a different way. The young man is heading for ordination, Anne and Peter believe, unaware of what goes on in Lia’s bedroom.

Lia’s body likes Matthew’s body – “her instructions had been written into his bones before birth” – but they are not good for one another. Harry, an academic, offers Lia the stability and optimism that Matthew cannot. He and Lia have a daughter, Iris. After recovering from breast cancer, Lia follows medical advice not to become pregnant again. The cancer returns anyway.

Maps of Our Spectacular Bodies, Maddie Mortimer’s ambitious, sprawling debut novel, centres on the relationship between mother and daughter at the end of Lia’s life. Iris is both sensitive – she comforts her mother with poetry and paintings – and strong, standing up to the girl at school who terrorises other children by revealing their secrets. But she cannot prevent Lia’s illness from bringing family secrets to the surface, which draw the nonlinear narrative back into the past.

Despite its title, not every character in Maps of Our Spectacular Bodies has a body. Lia shares the spotlight with “I, itch of ink, think of thing”, an impish, verbose and mysterious narrator that appears to be neither human nor nonhuman. Confined to its own short chapters early on, its signature bold type begins to infiltrate the standard third-person narration. In the final sections, the voice and Lia are inseparable. The hybrid character describes “the quiet passing of the I / into the vast and / boundless / you”.

The disorienting experience of this technique brings to mind Eimear McBride’s A Girl Is a Half-Formed Thing, another novel that stretches conventional language to address terminal illness. Whereas McBride’s prose is fragmented in a way that is consistent throughout, creating a distinctive stream-of-consciousness style, Mortimer’s writing is restlessly inventive. It includes different fonts, stanzas, visual arrangements, lists and playful definitions, without settling on a particular approach. Images are often both pleasing and convoluted, as when Iris considers growing up as a process of moving across from the world of her mother to the world of school in “a terrible act of osmosis”.

The novel is most involving where the body is intensely present – as in the often ambivalent sex between Lia and Matthew – or painfully absent, as in an excruciating scene on a train where a man attempts to grope Lia’s breasts, only to find that they have been removed. Embodied experience is important to the plot, which turns on revelations about blood ties. The exploration of different kinship relationships is delicate and persuasive.

But the focus is easily distracted. There is a passage during which sperm cells moving through a uterus are compared to the thousands of people forced to leave the Chernobyl exclusion zone in 1986. The voice set in bold type concludes the extended analogy by saying it is “a common misconception that creation and discovery don’t require / rather a lot of destruction”. In this context, harnessing the suffering of the former residents of Pripyat is bewildering.

Should the disembodied voice be interpreted as a personification of cancer? On the one hand, it explains with relish that “when pain replaces the proteins in [Lia’s] skin […] I’m in”. On the other hand, it knows a lot of trivia – about subjects ranging from Sex and the City to the nerve endings in the human clitoris, to female campers in Yellowstone national park – and makes very human, very lyrical pronouncements, such as that the cello is “the wisest instrument”.

The capriciousness of this voice is sharply funny, frustrating and genuinely odd. Sometimes it seems to attack the body and sometimes to be the body; sometimes it channels fear and sometimes it is the cause of fear. Occasionally, I heard its heckling as an expression of the writer’s own understandable unease. The publisher’s press release includes a letter from Mortimer herself, outlining the book’s origins in personal experience and expressing a hope that readers will be “gentle”. This is unnecessary. Maps of Our Spectacular Bodies sets its own terms, however strange and conflicted those terms may be.

• Maps of Our Spectacular Bodies by Maddie Mortimer is published by Picador (£14.99). To support the Guardian and the Observer buy a copy at guardianbookshop.com. Delivery charges may apply.