Hardware accelerators have been a promising solution to reduce the cost of cloud datacenters. This article investigates the acceleration of an important datacenter workload: the web server (or proxy) that faces high computational consumption originated from SSL/TLS processing and HTTP compression. Our study reveals that for the widely-deployed event-driven web architecture, the straight offloading of SSL/TLS or compression tasks suffers from frequent blockings in the offload I/O, leading to the underutilization of both CPU and accelerator resources. To achieve efficient acceleration, we propose QWEB, a comprehensive offload solution based on Intel QuickAssist Technology (QAT). QWEB introduces an asynchronous offload mode for SSL/TLS processing and a pipelining offload mode for HTTP compression, both allowing concurrent offload tasks from a single application process/thread. With these two novel offload modes, the blocking penalty is amortized or even eliminated, and the utilization rate of the parallel computation engines inside the QAT accelerator is greatly increased. The evaluation shows that QWEB provides up to 9x handshake performance with TLS-RSA (2048-bit) over the software baseline. Additionally, the secure data transfer throughput is enhanced by 2x for the SSL/TLS offloading only, 3.5x for the compression offloading only and 5x for the combined offloading.