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Invasive species pose one of the most serious global threats to biodiversity. Investigations into the interactions of native and non‐native species focus on the impacts of single species, despite being embedded in a network of direct and indirect interactions between multiple species and their environments.We developed 1‐km2 resolution, single‐species and multi‐species occupancy models using quantitative camera trap data collected by citizen scientists at 332 sites in a regional survey comprising the 14,130 km2 of Northern Ireland.Recent research suggests that native red and invasive grey squirrels in Britain and Ireland are linked by resource and disease‐mediated competition, and by a shared enemy, the European pine marten. We demonstrate that the presence of the pine marten reverses red squirrel replacement by grey squirrels on a regional basis, with red squirrel occupancy positively affected by exposure to pine marten. In contrast, the grey squirrel has a strongly negative response to the presence of pine marten.Modelling habitat suitability of pine marten and both squirrel species suggests that, despite the potentially strong effect of a recovering population of pine martens in controlling grey squirrel distribution, the latter is likely to persist in urban refugia that are either inaccessible or avoided by the pine marten.Synthesis and applications. Sustainable recovery of both the red squirrel and the pine marten across the wider landscapes of Ireland, Scotland and Northern England seems probable, while in Southern England and Wales, although possible, chances are more remote. Increasing native woodland cover on a landscape scale to facilitate pine marten recovery may assist in realizing this scenario. Despite the ongoing recovery of the pine marten, and resultant declines in grey squirrels, isolated populations are likely to persist in urban areas. Human‐lead control of grey squirrel populations in urban refugia requires urgent funding and implementation to avoid the development of novel genotypes in grey squirrel source populations that enable the species to better avoid predation by the pine marten. [ABSTRACT FROM AUTHOR]