The verse novel is a hybrid form in which a narrative with structural and stylistic similarities to a traditional novel is told through poetry.
From A Poet’s Glossary
The following additional definition of the term verse novel is reprinted from A Poet's Glossary by Edward Hirsch.
A novel in poetry. A hybrid form, the verse novel filters the devices of fiction through the medium of poetry. There are antecedents for the novelization of poetry in long narrative poems, in epics, chronicles, and romances, but the verse novel itself, as a distinct nineteenth-century genre, is different than the long poem that tells a story because it appropriates the discourse and language, the stylistic features of the novel as a protean form. Alexander Pushkin’s Eugene Onegin (1831) established the verse novel as a new type of poem in chapters and a new kind of novel in stanzas. Adam Mickiewicz’s twelve-book verse novel Pan Tadeusz (1834), which re-creates his Lithuanian childhood, stands at the top of nineteenth-century Polish literature. In English literature, the verse novel took different forms in the 1850s and ’60s in Elizabeth Barrett Browning’s fictional autobiography, Aurora Leigh (1856); in Arthur Clough’s epistolary fiction, Amours de Voyage (1857); in George Meredith’s sequence of sixteen-line sonnets, Modern Love (1862); and in Robert Browning’s series of dramatic monologues, The Ring and the Book (1868–1869). Unlike the Victorians, the modernist poets showed little interest in the verse novel, but contemporary poets have used it to gain for poetry some of the sweep and sensibility of prose fiction. My shortlist of contemporary self-described novels in verse includes Les Murray’s Fredy Neptune (1998), Anne Carson’s Autobiography of Red (1998), Vikram Seth’s The Golden Gate (1999), Brad Leithauser’s Darlington’s Fall (2002), Alice Notley’s Culture of One (2011), and Philip Schultz’s The Wherewithal (2013).