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A<sc>bstract</sc> We present a new class of interacting dark sector models that can address the Hubble tension. Interacting dark radiation (DR) has previously been put forward as a solution to the problem, but this proposal is disfavored by the high-ℓcosmic microwave background (CMB) data. We modify this basic framework by introducing a subcomponent of dark matter (DM) that interacts strongly with the DR, so that together they constitute a tightly coupled fluid at early times. We show that if this subcomponent decouples from the interacting DR during the CMB epoch, theℓmodes of the CMB that entered the horizon before decoupling are impacted differently from those that entered after, allowing a solution to the problem. We present a model that realizes this framework, which we dub “New Atomic Dark Matter”, or nuADaM, in which the interacting dark matter (iDM) subcomponent is composed of dark atoms, and dark “neutrinos” with long-range interactions contribute to the DR, hence the name of the model. This iDM subcomponent is acoustic at early times but decouples from the DR following dark recombination. In contrast to conventional atomic dark matter (ADM) models, the dark photon is part of a richer DR sector, which ensures that it continues to be self-interacting even after recombination. We show that this model admits a significantly larger value ofH₀than ΛCDM when fit to CMB and BAO data, while maintaining a comparable goodness of fit. Once the SHOES data set is included, it provides a significantly better fit than ΛCDM.