Engaging parents and children in family learning generates collaborative partnerships and can increase children's attainment, but headteachers' (HTs) views affect the nature of these Home-School Partnership (HSPs). This study into family-learning programmes (FLPs) in socio-economically disadvantaged areas in one Scottish city investigates what leads to more inclusive HSPs. Interviews were conducted in 2017 with 5 HTs, 7 family-learning practitioners (FLs) and 10 mothers. Previous research has found that if HTs hold a deficit conceptualisation of parents, this had a negative effect on their readiness to engage with the school. The authors' study found that this negativity could be mitigated by FLs because they fostered parents' own knowledge and realisation that they were important actors in their children's education. It presents an extended typology of HSPs -- "nominal," "traditional" and "authentic" -- that incorporates the influence of HTs, FLs and parents and shows how more equal HSPs might be developed.