A free-space optical access network with multiple ground stations (GSs) connected by a high-altitude platform (HAP) is proposed. The HAP plays a role of a two-way relay node that supports all-optical amplify-and-forward and half-duplex transmission. In the network, optical code-division multiple-access is utilized to enable asynchronous and simultaneous data transmission among GSs. In further steps of the study, the mathematical expressions of two system metrics including bit-error rate (BER) and network throughput are derived. They consider many physical layer impairments, such as power loss, atmospheric turbulence, pointing error, multiple-access interference, and receiver noise. Eventually, numerical results of the system performance under consideration of the number of GSs, the bit rate, and the received power confirm the feasibility of the proposed system as well as provide useful information for network design.