Context. Active galactic nuclei (AGNs) display complex X-ray spectra that exhibit a variety of emission and absorption features. These are commonly interpreted as a combination of (i) a relativistically smeared reflection component, resulting from the irradiation of an accretion disk by a compact hard X-ray source; (ii) one or several warm or ionized absorption components produced by AGN-driven outflows crossing our line of sight; and (iii) a nonrelativistic reflection component produced by more distant material. Disentangling these components via detailed model fitting could be used to constrain the black hole spin, geometry, and characteristics of the accretion flow, as well as of the outflows and surroundings of the black hole.Aims. We investigate how a high-throughput high-resolution X-ray spectrometer such as theAthenaX-ray Integral Field Unit (X-IFU) can be used to this aim, using the state-of-the-art reflection modelrelxillin a lamp-post geometrical configuration.Methods. We simulated a representative sample of AGN spectra, including all necessary model complexities, as well as a range of model parameters going from standard to more extreme values, and considered X-ray fluxes that are representative of known AGN and quasar populations. We also present a method to estimate the systematic errors related to the uncertainties in the calibration of the X-IFU.Results. In a conservative setting, in which the reflection component is computed self consistently by therelxillmodel from the pre-set geometry and no iron overabundance, the mean errors on the spin and height of the irradiating source are < 0.05 and ∼0.2R_g(in units of gravitational radius). Similarly, the absorber parameters (column density, ionization parameter, covering factor, and velocity) are measured to an accuracy typically less than ∼5% over their allowed range of variations. Extending the simulations to include blueshifted ultra-fast outflows, we show that X-IFU could measure their velocity with statistical errors < 1%, even for high-redshift objects (e.g., at redshifts ∼2.5).Conclusion. The simulations presented here demonstrate the potential of the X-IFU to understand how black holes are powered and how they shape their host galaxies. The accuracy in recovering the physical model parameters encoded in their X-ray emission is reached thanks to the unique capability of X-IFU to separate and constrain narrow and broad emission and absorption components.