Context. The X-ray transient eclipsing source MXB 1659−298 went into outburst in 1999 and 2015. During these two outbursts the source was observed by XMM-Newton, NuSTAR, and Swift/XRT. Aims. Using these observations, we studied the broadband spectrum of the source to constrain the continuum components and to verify whether it had a reflection component, as is observed in other X-ray eclipsing transient sources. Methods. We combined the available spectra to study the soft and hard state of the source in the 0.45–55 keV energy range. Results. We report a reflection component in the soft and hard state. The direct emission in the soft state can be modeled with a thermal component originating from the inner accretion disk plus a Comptonized component associated with an optically thick corona surrounding the neutron star. On the other hand, the direct emission in the hard state is described only by a Comptonized component with a temperature higher than 130 keV; this component is associated with an optically thin corona. We observed narrow absorption lines from highly ionized ions of oxygen, neon, and iron in the soft spectral state. We investigated where the narrow absorption lines form in the ionized absorber. The equivalent hydrogen column density associated with the absorber is close to 6 × 10²³ cm⁻² and 1.3 × 10²³ cm⁻² in the soft and hard state, respectively.