Semantic communication, when examined through the lens of joint source-channel coding (JSCC), maps source messages directly into channel input symbols, where the measure of success is defined by end-to-end distortion rather than traditional metrics such as block error rate. Previous studies have shown significant improvements achieved through deep learning (DL)-driven JSCC compared to traditional separate source and channel coding. However, JSCC is impractical in existing communication networks, where application and network providers are typically different entities connected over general-purpose TCP/IP links. In this paper, we propose designing the source and channel mappings separately and sequentially via a novel multi-level reliability interface. This conceptual interface enables semi-JSCC at both the learned source and channel mappers and achieves many of the gains observed in existing DL-based JSCC work (which would require a fully joint design between the application and the network), such as lower end-to-end distortion and graceful degradation of distortion with channel quality. We believe this work represents an important step towards realizing semantic communications in wireless networks.