A measurement of CP-violating observables associated with the interference of B0→ D0K⋆(892)0 and B0→D¯0K⋆8920 decay amplitudes is performed in the D0→ K∓π±(π+π−), D0→ π+π−(π+π−), and D0→ K+K− final states using data collected by the LHCb experiment corresponding to an integrated luminosity of 9 fb−1. CP-violating observables related to the interference of Bs 0→D0K¯⋆8920 and Bs 0→D¯0K¯⋆8920 are also measured, but no evidence for interference is found. The B0 observables are used to constrain the parameter space of the CKM angle γ and the hadronic parameters rB0 DK⋆ and δB0 DK⋆ with inputs from other measurements. In a combined analysis, these measurements allow for four solutions in the parameter space, only one of which is consistent with the world average.