Values for the two-photon absorption coefficient, ${\alpha }_2$ , and nonlinear refractive index coefficients, $n_2$ , are measured for a waveguide core made of 14:14 monolayer $\mathrm{GaAs}∕\mathrm{AlAs}$ superlattice at photon energies below the half-bandgap. Two-photon absorption coefficients show significant anisotropy with the TE mode having ${\alpha }_2$ values up to four times greater than the TM mode. For nonlinear refraction, we determined values of the nonlinear index for the TE mode that are as much as two times larger than the TM mode. Measurements of cross-phase modulation between the TE and TM modes gave ratios of cross-phase modulation to self-phase modulation that were highly anisotropic.