During hybrid speciation, homoeologues combine in a single genome. Homoeologue expression bias (HEB) occurs when one homoeologue has higher gene expression than another. HEB has been well characterized in plants but rarely investigated in animals, especially invertebrates. Consequently, we have little idea as to the role that HEB plays in allopolyploid invertebrate genomes. If HEB is constrained by features of the parental genomes, then we predict repeated evolution of similar HEB patterns among hybrid genomes formed from the same parental lineages. To address this, we reconstructed the history of hybridization between the New Zealand stick insect genera Acanthoxyla and Clitarchus using a high-quality genome assembly from Clitarchus hookeri to call variants and phase alleles. These analyses revealed the formation of three independent diploid and triploid hybrid lineages between these genera. RNA sequencing revealed a similar magnitude and direction of HEB among these hybrid lineages, and we observed that many enriched functions and pathways were also shared among lineages, consistent with repeated evolution due to parental genome constraints. In most lineages, a slight majority of the genes involved in mitochondrial function showed HEB towards the maternal homoeologues, consistent with only weak effects of mitonuclear incompatibility. We also observed a proteasome functional enrichment in most lineages and hypothesize this may result from the need to maintain proteostasis in hybrid genomes. Reference bias was a pervasive problem, and we caution against relying on HEB estimates from a single parental reference genome.