Context. The iron lines at 630.15 and 630.25 nm are often used to determine the physical conditions of the solar photosphere. A common approach is to invert them simultaneously under the Milne-Eddington approximation. The same thermodynamic parameters are employed for the two lines, except for their opacities, which are assumed to have a constant ratio. Aims: We aim at investigating the validity of this assumption, since the two lines are not exactly the same. Methods: We use magnetohydrodynamic simulations of the quiet Sun to examine the behavior of the ME thermodynamic parameters and their influence on the retrieval of vector magnetic fields and flow velocities. Results: Our analysis shows that the two lines can be coupled and inverted simultaneously using the same thermodynamic parameters and a constant opacity ratio. The inversion of two lines is significantly more accurate than single-line inversions because of the larger number of observables.