The crystallographic structure of the cuprate Sr14Cu24O41 is a misfit stacking of layers of two distinct quantum-spin systems: linear edge-sharing CuO2 chains and 2-leg Cu2O3 spin-ladders. Interestingly, the CuO2-chains contain a large amount of holes which give rise to a quasi-2D charge order at low temperature, associated with a strong lattice distortion. In order to understand better the nature of excitation spectra in both sub-systems (in particular their possible hybrid or orbital nature), we have recently performed accurate polarimetric inelastic-neutron-scattering studies of the chain and ladder excitations in Sr14Cu24O41 as a function of both the wave vector and the temperature. By measuring the spin-flip and non-spin-flip contributions for the incident polarization applied parallel and perpendicular to the scattering vector Q we have been able to separate the nuclear and the various magnetic components. Quite unexpectedly, our results for the CuO2 chains and Cu2O3 ladders reveal the existence of a strong anisotropy of the magnetic inelastic structure factors, which could be the signature of orbital currents theoretically predicted.