The development of robust production processes is essential for the introduction of advanced materials based on renewable and Earth-abundant resources. Cellulose nanomaterials have been combined with other highly available nanoparticles, in particular clays, to generate multifunctional films and foams. Here, the structure of dispersions of rod-like cellulose nanocrystals (CNC) and montmorillonite nanoplatelets (MNT) was probed using small-angle X-ray scattering within a rheological cell (Rheo-SAXS). Shear induced a high degree of particle orientation in both the CNC-only and CNC:MNT composite dispersions. Relaxation of the shear-induced orientation in the CNC-only dispersion decayed exponentially and reached a steady-state within 20 seconds, while the relaxation of the CNC:MNT composite dispersion was found to be strongly retarded and partially inhibited. Viscoelastic measurements and Guinier analysis of dispersions at the shear rate of 0.1 s-1 showed that the addition of MNT promotes gel formation of the CNC:MNT composite dispersions. A better understanding of shear-dependent assembly and orientation of multi-component nanoparticle dispersions can be used to process materials with improved mechanical and functional properties.