Efficient data transmission across mobile multi-hop networks that connect edge devices to core servers presents significant challenges, particularly due to the variability in link qualities between wireless and wired segments. This variability necessitates a robust transmission scheme that transcends the limitations of existing deep joint source-channel coding (DeepJSCC) strategies, which often struggle at the intersection of analog and digital methods. Addressing this need, this paper introduces a novel hybrid DeepJSCC framework, h-DJSCC, tailored for effective image transmission from edge devices through a network architecture that includes initial wireless transmission followed by multiple wired hops. Our approach harnesses the strengths of DeepJSCC for the initial, variable-quality wireless link to avoid the cliff effect inherent in purely digital schemes. For the subsequent wired hops, which feature more stable and high-capacity connections, we implement digital compression and forwarding techniques to prevent noise accumulation. This dual-mode strategy is adaptable even in scenarios with limited knowledge of the image distribution, enhancing the framework's robustness and utility. Extensive numerical simulations demonstrate that our hybrid solution outperforms traditional fully digital approaches by effectively managing transitions between different network segments and optimizing for variable signal-to-noise ratios (SNRs). We also introduce a fully adaptive h-DJSCC architecture capable of adjusting to different network conditions and achieving diverse rate-distortion objectives, thereby reducing the memory requirements on network nodes.