The ab initio investigation of the magnetic ordering in digital alloys consisting of monolayers of 3d-transition metals Ti, V, Cr, Mn, Fe, Co, and Ni introduced into the Si, Ge, and Si_0.5Ge_0.5 semiconductor hosts is reported. The calculations of the parameters of the exchange interactions and total-energy calculations indicate that the ferromagnetic order appears only in the manganese monolayers, whereas the antiferromagnetic order is more probable in V, Cr, and Fe monolayers, and Ti, Co, and Ni monolayers are nonmagnetic. The stability of the ferromagnetic phase in digital alloys containing manganese monolayers has been analyzed using the calculations of magnon spectra.