Breeding pigs that can efficiently digest alternative diets with increased fibre content is a viable strategy to mitigate the feed cost volatility in pig production. This study aimed at determining the relative contribution of microbiome and genetics to the phenotypic variability of three digestibility coefficients (DC). Faecal samples were collected at sixteen weeks of age to sequence the V3-V4 regions of the 16S RNA gene and to predict DC with near-infrared spectrometry for energy, organic matter, and nitrogen. Data were available for 1,564 Large White pigs, and 14,366 identified Operational Taxonomic Units (OTUs) were identified. The proportions of phenotypic variance explained by the microbiome, or ‘microbiability’, and by additive genetic effects were first estimated independently and then jointly using a Bayesian approach. The microbiability was estimated under three scenarios: without filtering the OTUs, by filtering the OTUs presented in more than five samples and with an average abundance higher than 0.001% (2,399 OTUs) or greater than 0.01% (803 OTUs). Estimates of microbiability for the traits were reduced with increasingly stringent filtering, from 54±2 to 66±2% in the first scenario and from 25±1 to 35±1% for 803 OTUs. With intermediate filtering, the estimated microbiability ranged from 37±1 to 46±2% and was higher than heritability (from 26±1 to 29±1%) when estimated independently from genetics effects. The joint estimation of microbiability and heritability will point out how the two random effects overlap in explaining the trait variability. To conclude, our results show that the filtering of OTUs is important and influences microbiability. The microbiome explained a significant proportion of the phenotypic variance of digestive efficiency, which was even larger than heritability estimates.