Indirect interactions as mediated by higher and lower trophic levels have been advanced as key forces structuring herbivorous arthropod communities around the globe. Here, we present a first quantification of the interaction structure of a herbivore-centered food web from the High Arctic. Targeting the Lepidoptera of Northeast Greenland, we introduce generalized overlap indices as a novel tool for comparing different types of indirect interactions. First, we quantify the scope for top-down-up interactions as the probability that a herbivore attacking plant species i itself fed as a larva on species j. Second, we gauge this herbivore overlap against the potential for bottom-up-down interactions, quantified as the probability that a parasitoid attacking herbivore species i itself developed as a larva on species j. Third, we assess the impact of interactions with other food web modules, by extending the core web around the key herbivore Sympistis nigrita to other predator guilds (birds and spiders). We find the host specificity of both herbivores and parasitoids to be variable, with broad generalists occurring in both trophic layers. Indirect links through shared resources and through shared natural enemies both emerge as forces with a potential for shaping the herbivore community. The structure of the host-parasitoid submodule of the food web suggests scope for classic apparent competition. Yet, based on predation experiments, we estimate that birds kill as many (8%) larvae of S. nigrita as do parasitoids (8%), and that spiders kill many more (38%). Interactions between these predator guilds may result in further complexities. Our results caution against broad generalizations from studies of limited food web modules, and show the potential for interactions within and between guilds of extended webs. They also add a data point from the northernmost insect communities on Earth, and describe the baseline structure of a food web facing imminent climate change.