The microscopic anharmonic vibrator approach (MAVA) is a scheme where the one- and two-phonon states of an even–even nucleus are treated consistently by using a realistic microscopic nuclear Hamiltonian. This model has recently been extended to describe odd–odd nuclei by adding proton–neutron phonons in a scheme called the proton–neutron MAVA (pnMAVA). In this paper, we apply pnMAVA to compute the nuclear matrix elements corresponding to the two-neutrino double beta (2νββ) decay of ¹⁰⁰Mo to the ground state and the first excited 0⁺ state of ¹⁰⁰Ru in a realistic single-particle space. We also compute the GT− and GT+ Gamow–Teller strength functions and compare them with the plain pnQRPA (proton–neutron QRPA) and available data. The redistribution of strength to four-quasiparticle degrees of freedom can be clearly seen in the GT+ function. The more striking effect is seen in the 2νββ matrix element corresponding to the ground-state transition where the incoherence of individual contributions is stronger for the pnMAVA than for the pnQRPA, and a 15% reduction in the magnitude of the matrix element is obtained for the pnMAVA. The 2νββ transition rate to the excited 0⁺ state is zero in a pnQRPA calculation, whereas the pnMAVA result is not far from the measured decay rate.