The widespread adoption of communication and control infrastructures will not only improve the microgrid system performance in normal conditions but also increase microgrid cybersecurity risks. Potential cyberattacks can deteriorate microgrid performances by corrupting and intercepting data exchanges among participating DERs, whereby microgrids deviate from desired operating conditions and stable microgrid operations are jeopardized. In this paper, a cross-layer control strategy is proposed to enhance the microgrid resilience against false data injection (FDI) and denial of service (DoS) attacks. On the one hand, the proposed control strategy will not interfere with microgrid normal operations when there are no cyberattacks. On the other hand, the proposed control strategy can effectively mitigate the impacts of FDI and DoS attacks on microgrids without relying on prompt detection and isolation of cyberattacks. The stability of the proposed control strategy is demonstrated using the Lyapunov theory under different scenarios, including without and with FDI and DoS attacks. The effectiveness of the proposed cross-layer resilient control strategy against cyberattacks is validated in a 12-bus microgrid system using time-domain PSCAD/EMTDC simulations.