The present study is concerned with the reflection of magneto-thermoelastic plane waves from stress free and thermally insulated surface in a homogeneous isotropic thermally conducting elastic half-space medium. The modified Green–Lindsay (MGL) theory of generalized thermoelasticity has employed with two temperatures (2 T). The thermoelastic coupling effect creates two types of coupled longitudinal waves which are dispersive as well as exhibit attenuation. There exist also due to the thermoelastic coupling one independent vertically shear (SV-wave) wave. In contrast to the classical Green–Lindsay (GL) and Lord–Shulman (LS) theories of generalized thermoelasticity, the SV-wave is not only dispersive in nature but also experiences attenuation. Analytical expressions for the reflection coefficients and their respective energy ratios for reflected thermoelastic waves have been determined when the coupled longitudinal wave incident on the free surface. A numerical result on the reflection coefficients and their respective energy ratios for the specific parameter has been calculated. Various graphs have been plotted to analyze the behavior of these quantities. The characteristics of employing the 2TMGL model are discussed by comparing the numerical results obtained for the present model with those in the classical GL model. © 2020, © 2020 Taylor & Francis Group, LLC.