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Context. It is known that Alfvén 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 Alfvén 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 Alfvén 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 Alfvén and magnetoacoustic waves can significantly contribute to the heating of the solar chromosphere and to the generation of plasma outflows.