Engineering the electromagnetic environment of a quantum emitter gives rise to a plethora of exotic light -matter interactions. In particular, photonic lattices can seed long-lived atom-photon bound states inside photonic band gaps. Here, we report on the concept and implementation of a novel microwave architecture consisting of an array of compact superconducting resonators in which we have embedded two frequency -tunable artificial atoms. We study the atom-field interaction and access previously unexplored coupling regimes, in both the single-and double-excitation subspace. In addition, we demonstrate coherent interactions between two atom-photon bound states, in both resonant and dispersive regimes, that are suitable for the implementation of SWAP and CZ two-qubit gates. The presented architecture holds promise for quantum simulation with tunable-range interactions and photon transport experiments in the nonlinear regime.