Traditional discrete-array-based systems fail to exploit interactions between closely spaced antennas, resulting in inadequate utilization of the aperture resource. In this paper, we propose a holographic intelligence surface (HIS) assisted integrated sensing and communication (HISAC) system, wherein both the transmitter and receiver are fabricated using a continuous-aperture array. A continuous-discrete transformation of the HIS pattern based on the Fourier transform is proposed, converting the continuous pattern design into a discrete beamforming design. We formulate a joint transmit-receive beamforming optimization problem for the HISAC system, aiming to balance the performance of multi-target sensing while fulfilling the performance requirement of multi-user communication. To solve the non-convex problem with coupled variables, an alternating optimization-based algorithm is proposed to optimize the HISAC transmit-receive beamforming in an alternate manner. Specifically, the transmit beamforming design is solved by decoupling into a series of feasibility-checking sub-problems while the receive beamforming is determined by the Rayleigh quotient-based method. Simulation results demonstrate the superiority of the proposed HISAC system over traditional discrete-array-based ISAC systems, achieving significantly higher sensing performance while guaranteeing predetermined communication performance.