By using the genotyping-by-sequencing method, it is feasible to characterize genomic relationships directly at the level of family pools and to estimate genomic heritabilities from phenotypes scored on family-pools in outbreeding species. Genotyping-by-sequencing (GBS) has recently become a promising approach for characterizing plant genetic diversity on a genome-wide scale. We use GBS to extend the concept of heritability beyond individuals by genotyping family-pool samples by GBS and computing genomic relationship matrices (GRMs) and genomic heritabilities directly at the level of family-pools from pool-frequencies obtained by sequencing. The concept is of interest for species where breeding and phenotyping is not done at the individual level but operates uniquely at the level of (multi-parent) families. As an example we demonstrate the approach using a set of 990 two-parent F2 families of perennial ryegrass (Lolium Perenne). The families were phenotyped as a family-unit in field plots for heading date and crown rust resistance. A total of 728 K single nucleotide polymorphism (SNP) variants were available and were divided in groups of different sequencing depths. GRMs based on GBS data showed diagonal values biased upwards at low sequencing depth, while off-diagonals were little affected by the sequencing depth. Using variants with high sequencing depth, genomic heritability for crown rust resistance was 0.33, and for heading date 0.22, and these genomic heritabilities were biased downwards when using variants with lower sequencing depth. Broad sense heritabilities were 0.61 and 0.66, respectively. Underestimation of genomic heritability at lower sequencing depth was confirmed with simulated data. We conclude that it is feasible to use GBS to describe relationships between family-pools and to estimate genomic heritability directly at the level of F2 family-pool samples, but estimates are biased at low sequencing depth.