A power-balanced hybrid optical imaging system has a diffractive computational camera, introduced in this paper, with image formation by a refractive lens and multilevel phase mask (MPM). This system provides a long focal depth with low chromatic aberrations thanks to MPM and a high energy light concentration due to the refractive lens. We introduce the concept of optical power balance between the lens and MPM, which controls the contribution of each element to modulate the incoming light. Additional features of our MPM design are the inclusion of the quantization of the MPM's shape on the number of levels and the Fresnel order (thickness) using a smoothing function. To optimize the optical power balance as well as the MPM, we built a fully differentiable image formation model for joint optimization of optical and imaging parameters for the proposed camera using neural network techniques. We also optimized a single Wiener-like optical transfer function (OTF) invariant to depth to reconstruct a sharp image. We numerically and experimentally compare the designed system with its counterparts, lensless and just-lens optical systems, for the visible wavelength interval (400-700) nm and the depth-of-field range (0.5-∞ m for numerical and 0.5-2 m for experimental). We believe the attained results demonstrate that the proposed system equipped with the optimal OTF overcomes its counterparts--even when they are used with optimized OTF--in terms of the reconstruction quality for off-focus distances. The simulation results also reveal that optimizing the optical power balance, Fresnel order, and the number of levels parameters are essential for system performance attaining an improvement of up to 5 dB of PSNR using the optimized OTF compared to its counterpart lensless setup.