A multi-chip package that includes multiple integrated circuits is provided. An integrated circuit in the multi-chip package may be mounted on an interposer. The interposer may be mounted on a package substrate. The integrated circuit may have internal power supply terminals coupled to on-package decoupling (OPD) capacitor circuitry that are formed as part of the package substrate. The power supply terminals on the integrated circuit may be coupled to conductive routing paths and through-silicon vias (TSVs) in the interposer via microbumps. The through-silicon vias in the interposer may be coupled to the OPD capacitor circuitry via flip-chip bumps. The conductive routing paths and the TSVs in the interposer may be coupled to the internal integrated circuit power supply terminals in a way that minimizes power supply resonance noise.