In dairy cattle, the rate of genetic gain from genomic selection depends on reliability of direct genomic values (DGV). One option to increase reliabilities could be to increase the size of the reference set used for prediction, by using genotyped bulls with daughter information in countries other than the evaluating country. The increase in reliabilities of DGV from using this information will depend on the extent of genotype by environment interaction between the evaluating country and countries contributing information, and whether this is correctly accounted for in the prediction method. As the genotype by environment interaction between Australia and Europe or North America is greater than between Europe and North America for most dairy traits, ways of including information from other countries in Australian genomic evaluations were examined. Thus, alternative approaches for including information from other countries and their effect on the reliability and bias of DGV of selection candidates were assessed. We also investigated the effect of including overseas (OS) information on reliabilities of DGV for selection candidates that had weaker relationships to the current Australian reference set. The DGV were predicted either using daughter trait deviations (DTD) for the bulls with daughters in Australia, or using this information as well as OS information by including deregressed proofs (DRP) from Interbull for bulls with only OS daughters in either single trait or bivariate models. In the bivariate models, DTD and DRP were considered as different traits. Analyses were performed for Holstein and Jersey bulls for milk yield traits, fertility, cell count, survival, and some type traits. For Holsteins, the data used included up to 3,580 bulls with DTD and up to 5,720 bulls with only DRP. For Jersey, about 900 bulls with DTD and 1,820 bulls with DRP were used. Bulls born after 2003 and genotyped cows that were not dams of genotyped bulls were used for validation. The results showed that the combined use of DRP on bulls with OS daughters only and DTD for Australian bulls in either the single trait or bivariate model increased the coefficient of determination [(R(2)) (DGV,DTD)] in the validation set, averaged across 6 main traits, by 3% in Holstein and by 5% in Jersey validation bulls relative to the use of DTD only. Gains in reliability and unbiasedness of DGV were similar for the single trait and bivariate models for production traits, whereas the bivariate model performed slightly better for somatic cell count in Holstein. The increase in R(2) (DGV,DTD) as a result of using bulls with OS daughters was relatively higher for those bulls and cows in the validation sets that were less related to the current reference set. For example, in Holstein, the average increase in R(2) for milk yield traits when DTD and DRP were used in a single trait model was 23% in the least-related cow group, but only 3% in the most-related cow group. In general, for both breeds the use of DTD from domestic sources and DRP from Interbull in a single trait or bivariate model can increase reliability of DGV for selection candidates.