We present a theoretical study of all-optical magnetization switching in rare-earth/transition-metal bilayer, $\mathrm{R}{\mathrm{E}}_{n}/\mathrm{T}{\mathrm{M}}_{m}$, consisting of $n$ RE monolayers and $m$ TM monolayers. Using the Landau-Lifshitz-Bloch equation, we numerically calculate the spin dynamics, including spin transport in the bilayer, upon incidence of a single laser pulse. It is shown that the spin transfer between the RE and TM layers with $n>1$ or $m>1$ is necessary for the switching. The calculation shows that the spin transfer makes conditions for the switching similar to those for the ferrimagnetic alloys. When the spin transfer between the monolayers is absent the intensity of the exchange scattering decreases and the switching is possible only in the $\mathrm{R}{\mathrm{E}}_{1}/\mathrm{T}{\mathrm{M}}_{1}$ bilayer. A relationship between the spin relaxation and temperature dependence of the switching is discussed.
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