A key goal of bottom-up synthetic biology is to construct cell- and tissue-like structures. Underpinning cellular life is the ability to process several external chemical signals, often in parallel. Until now, however, cell- and tissue-like structures have only been constructed with one signalling pathway. Here, we construct a dual-signal processor from the bottom up in a modular fashion. The processor comprises three aqueous compartments bounded by lipid bilayers and operates in an aqueous environment. It can receive two chemical signals from the external environment, process them orthogonally, and then produce a distinct output for each signal. It is suitable for both sensing and enzymatic processing of environmental signals with fluorescence and molecular outputs. In the future, such processors could serve as smart drug delivery vehicles or as modules within synthetic tissues to control their behaviour in response to external chemical signals.