  Context. It is known that Alfv\'en and magnetoacoustic waves both contribute
to the heating of the solar chromosphere and drive plasma outflows. In both
cases, the thermalization of the wave energy occurs due to ion-neutral
collisions, but the obtained rates of plasma heating cannot explain the
observational data. The same is true for the magnitudes of the outflows.
  Aims. The aim of the present paper is to reexamine two-fluid modeling of
Alfv\'en and magnetoacoustic waves in the partially ionized solar chromosphere.
We attempt to detect variations in the ion temperature, and vertical plasma
flows for different wave combinations.
  Methods. We performed numerical simulations of the generation and evolution
of coupled Alfv\'en and magnetoacoustic waves using the JOANNA code, which
solves the two-fluid equations for ions (protons)+electrons and neutrals
(hydrogen atoms), coupled by collision terms.
  Results. We confirm that the damping of impulsively generated small-amplitude
waves negligibly affects the chromosphere temperature and generates only slow
plasma flows. In contrast, waves generated by large-amplitude pulses
significantly increase the chromospheric temperature and result in faster
plasma outflows. The maximum heating occurs when the pulse is launched from the
center of the photosphere, and the magnitude of the related plasma flows
increases with the amplitude of the pulse. Conclusions. Large-amplitude coupled
two-fluid Alfv\'en and magnetoacoustic waves can significantly contribute to
the heating of the solar chromosphere and to the generation of plasma outflows.
