We report the strong coupling between plasmonic surface lattice resonances (SLRs) and photonic Fabry-Pérot (F-P) resonances in a microcavity embedded with two-dimensional periodic array of metal-insulator-metal nanopillars. For such a plasmonic-photonic system, we show that the SLR can be strongly coupled to the F-P resonances of both the odd- and even orders, and that the splitting energy reaches as high as 138 meV in the visible regime. We expect that this work will provide a new scheme for strong coupling between plasmonic and photonic modes.