We report on the structural and microscopic superconducting properties of the Ca1−xSrxAlSi solid solution. Specifically, we have realized the continuous solid solution, which for all members, other than x=0 (CaAlSi), crystallizes in the AlB2-type structure. For CaAlSi, we present an improved structural model where all Al/Si layers are buckled, leading to a 6-folded structure along the crystallographic c direction. We, furthermore, find indications for the structural instability in the parent compound CaAlSi to enhance the superconductivity across the solid solution. Our investigation of the magnetic penetration depths by means of muon-spin rotation experiments reveals that CaAlSi is a two-gap superconductor, that SrAlSi is a single-gap superconductor, and that there is a continuous transition from one electronic state to the other across the solid solution. Hence, we show that the Ca1−xSrxAlSi solid solution is a highly tunable two-gap to single-gap superconducting system on a honeycomb lattice, where the superconductivity is strongly connected to a structural instability, i.e., the buckling of the Al/Si layers.