Two doubly interpenetrated coordination polymers [Co2(BDC)2(bpt)2]·nSolvent based on dimeric secondary building units and crystallizing with distinct solvent molecules (-H2O and -MeOH for nSolvent = 2H2O and MeOH·H2O, respectively) were obtained by employing 1,4-benzenedicarboxylate (BDC) and 1H-3,5-bis(4-pyridyl)-1,2,4-triazole) (bpt) as linkers. The structures consist of a square grid of dimers bridged by BDC and pillared by bpt. Thermogravimetry and PXRD indicate that the frameworks are stable and are retained up to 400 °C, but the structures are modified irreversibly. -H2O, high-symmetry Pna21, exhibits antiferromagnetic coupling within the dimer, while -MeOH, low-symmetry P21/n, exhibits ferromagnetic coupling. Upon desolvation, the -de and -de couplings are antiferromagnetic but reduced. Subsequent resolvation to -H2O and -MeOH resulted in a slight increase of the antiferromagnetic coupling without attaining the virgin states. The interesting difference of magnetic properties between -H2O and -MeOH, the solvated/desolvated phases, particularly at low temperature, indicates that there is a prominent solvent effect.