The nonlinear optical response of common materials is limited by bandwidth and energy consumption, which impedes practical application in all-optical signal processing, light detection, harmonic generation, etc. Additionally, the nonlinear performance is typically sensitive to polarization. To circumvent this constraint, we propose that orthogonal nanoantennas coupled to Al-doped zinc oxide (AZO) epsilon-near-zero (ENZ) material show a broadband (~1000 nm bandwidth) large optical nonlinearity simultaneously for two orthogonal polarization states. The absolute maximum value of the nonlinear refractive index n(2) is 7.65 cm(2)center dot GW(-)(1), which is 4 orders of magnitude larger than that of the bare AZO film and 7 orders of magnitude larger than that of silica. The coupled structure not only realizes polarization independence and strong nonlinearity, but also allows the sign of the nonlinear response to be flexibly tailored. It provides a promising platform for the realization of ultracompact, low-power, and highly nonlinear all-optical devices on the nanoscale.