A large proportion of genetic variations involved in complex diseases are rare and located within non-coding regions, making the interpretation of underlying biological mechanisms difficult. Although technical and methodological progresses have been made to annotate the genome, current disease- rare-variant association tests incorporating such annotations suffer from two major limitations. Firstly, they are restricted to case-control designs of unrelated individuals, which often require tens or hundreds of thousands of individuals to achieve sufficient power. Secondly, they were not evaluated with region-based annotations needed to interpret the causal regulatory mechanisms. In this work we propose RetroFun-RVS, a new retrospective family-based score test, incorporating functional annotations. One of the critical features of the proposed method is to aggregate genotypes while measuring rare variant sharing among affected family members to compute the test statistic. Through extensive simulations, we have demonstrated that RetroFun-RVS integrating networks based on 3D genome contacts as functional annotations reaches greater power over the region-wide test, others strategies to include sub-regions and competing methods. Also, the proposed framework shows robustness to non-informative annotations, keeping a stable power when causal variants are spread across regions. We provide recommendations when dealing with different types of annotations or family structures commonly encountered in practice. In summary we argue that RetroFun-RVS, by allowing integration of functional annotations corresponding to regions or networks with transcriptional impacts, is a useful framework to highlight regulatory mechanisms involved in complex diseases.