In addition to including one of the most popular companion animals, species from the cat family Felidae serve as a powerful system for genetic analysis of inherited and infectious disease, as well as for the study of phenotypic evolution and speciation. Previous diploid-based genome assemblies for the domestic cat have served as the primary reference for genomic studies within the cat family. However, these versions suffered from poor resolution of complex and highly repetitive regions, with substantial amounts of unplaced sequence that is polymorphic or copy number variable. We sequenced the genome of a female F1 Bengal hybrid cat, the offspring of a domestic cat (Felis catus) x Asian leopard cat (Prionailurus bengalensis) cross, with PacBio long sequence reads and used Illumina sequence reads from the parents to phase >99.9% of the reads into the two species’ haplotypes. De novo assembly of the phased reads produced highly continuous haploid genome assemblies for the domestic cat and Asian leopard cat, with contig N50 statistics exceeding 83 Mb for both genomes. Whole genome alignments reveal the Felis and Prionailurus genomes are colinear, and the cytogenetic differences between the homologous F1 and E4 chromosomes represent a case of centromere repositioning in the absence of a chromosomal inversion. Both assemblies offer significant improvements over the previous domestic cat reference genome, with a 100% increase in contiguity and the capture of the vast majority of chromosome arms in one or two large contigs. We further demonstrated that comparably accurate F1 haplotype phasing can be achieved with members of the same species when one or both parents of the trio are not available. These novel genome resources will empower studies of feline precision medicine, adaptation and speciation.