Human genomes are typically assembled as consensus sequences that lack information on parental haplotypes. Here we describe a reference-free workflow for diploid de novo genome assembly that combines the chromosome-wide phasing and scaffolding capabilities of single-cell strand sequencing with continuous long-read or high-fidelity sequencing data. Employing this strategy, we produced a completely phased de novo genome assembly for each haplotype of an individual of Puerto Rican descent (HG00733) in the absence of parental data. The assemblies are accurate (quality value > 40) and highly contiguous (contig N50 > 23 Mbp) with low switch error rates (0.17%), providing fully phased single-nucleotide variants, indels and structural variants. A comparison of Oxford Nanopore Technologies and Pacific Biosciences phased assemblies identified 154 regions that are preferential sites of contig breaks, irrespective of sequencing technology or phasing algorithms.