We theoretically study the ionization enhancement of the diatomic molecular ion H₂⁺ at two critical internuclear distances R, using orthogonal two-color laser fields. The polarization of the fundamental infrared laser field and a weak second-harmonic field is parallel and perpendicular to the molecular axis, respectively. It is observed that adding the second-harmonic field raises slightly the first ionization peak at the smaller critical R, whereas it enhances the second one at the larger critical R significantly. We further analyze the observable evidence which distinguishes two underlying mechanisms responsible for the enhanced ionization of H₂⁺: (i) the resonant excitation along with the coherent interference of the ionizing wave packets from the 1sσ_g and 2pσ_u states and (ii) the easier ionization from the up-field site of the molecule.