The aspheric test via finite distance null compensation is limited by too many adjustment factors and low test precision. Here we establish an aspheric test system by integrating front null compensation with back null compensation, in which a compensation lens is used before and after the spherical center of the mirror to be tested and thus the front and back areas show aberration correlation. First, based on the aberration theory, the optical parameters of two compensation lenses are theoretically derived and solved, and the relationship between the initial parameters and the normalized data is analyzed. Then the normalized results are scaled and optimized by the optical design software. Four concave parabolic mirrors with different curvature radii are designed under different magnifications of front null compensation lenses. The maximum aperture and the maximum relative aperture of the aspheric mirror are obtained. The compensation lens with a 1/10 aperture ratio is used to realize the aspheric test of an aspheric mirror with a large aperture of 3.7 m and a large relative aperture of 1/1.2, and the peak-valley (PV) value of the residual wavefront error is superior to 0.1λ (λ=633 nm). The tolerance analysis confirms that the test system is feasible. The principle experiment is conducted for the parabolic mirror with an aperture of 500 mm and a relative aperture of 1/1. The maximum diameter of the aspheric mirror and the difficulty of implementation are compared between the proposed method and the classical configuration. The PV value and the RMS value of the designed wavefront error of the test system combining front and back null compensation is 0.061λ and 0.009λ, respectively. The RMS value is superior to λ/40. The test system combining front and back null compensation is suitable for the high-precision test of aspheric surfaces with 4 m large diameter and large relative aperture.