Integrated sensing and communication (ISAC) system has been emerged as a crucial paradigm for addressing the growing demand of emerging wireless applications that require both ultra-reliable data transmission and high-precision sensing. However, due to the limited computation capability of ISAC devices, the large amount of collected sensing data is difficult to be timely processed. In this paper, we consider that the ISAC device can offload the sensing data to a group edge helper nodes via multi-access edge computing to improve the efficiency of sensing data processing. We propose a multi-access edge computing empowered ISAC with hybrid active and passive sensing, in which the ISAC device can perform passive sensing through the sensing reflected signal from the edge helper nodes while performing active sensing. To investigate this problem, we formulate a joint optimization of the transmit beamforming for active sensing, passive sensing and offloading, as well as the computation rates of both the ISAC device and the edge helper nodes, with the objective of maximizing the total computation rates for the sensing data. Despite the non-convexity of the formulated problem, we propose an efficient algorithm to obtain its solutions. Simulation results validate the performance advantages of our multi-access edge computing empowered integrated hybrid sensing and communication.