Michelson-type laser-interferometric gravitational-wave (GW) observatories employ very high light powers as well as transmissively-coupled Fabry-Perot arm resonators in order to realize high measurement sensitivities. Due to the absorption in the transmissive optics, high powers lead to thermal lensing and hence to thermal distortions of the laser beam profile, which sets a limit on the maximal light power employable in GW observatories. Here, we propose and realize a Michelson-type laser interferometer with arm resonators whose coupling components are all-reflective second-order Littrow gratings. In principle such gratings allow high finesse values of the resonators but avoid bulk transmission of the laser light and thus the corresponding thermal beam distortion. The gratings used have three diffraction orders, which leads to the creation of a second signal port. We theoretically analyze the signal response of the proposed topology and show that it is equivalent to a conventional Michelson-type interferometer. In our proof-of-principle experiment we generated phase-modulation signals inside the arm resonators and detected them simultaneously at the two signal ports. The sum signal was shown to be equivalent to a single-output-port Michelson interferometer with transmissively-coupled arm cavities, taking into account optical loss. The proposed and demonstrated topology is a possible approach for future all-reflective GW observatory designs.