In this talk, I study the non-relativistic limit of the Dirac equation for mixed neutrinos. A thorough analysis demonstrates that such a procedure inevitably leads to a redefinition of the inertial mass. This happens because, in contrast to the usual unmixed situations, the antiparticle sector contribution cannot be neglected. Furthermore, one can show that, when a gravitational interaction is switched on, in the weak-field approximation the mass parameter which couples to gravity (gravitational mass) does not undergo the same reformulation as the inertial mass; hence, the breakdown of the weak equivalence principle is unavoidable.