From a variational action with nonminimal coupling with a scalar field and classical scalar and fermionic interaction, cosmological field equations can be obtained. Imposing a Friedmann-Lemaitre-Robertson-Walker (FLRW) metric, the equations lead directly to a cosmological model consisting of two interacting fluids, where the scalar field fluid is interpreted as dark energy and the fermionic field fluid is interpreted as dark matter. Several cases were studied analytically and numerically. An important feature of the nonminimal coupling is that it allows crossing the barrier from a quintessence to phantom behavior. The insensitivity of the solutions to one of the parameters of the model permits it to find an almost analytical solution for the cosmological constant type of universe.