The concurrent self-assembly of new 1,3,5-trisamide-cyclohexane-based low molecular weight hydrogelators and various surfactants in water leads to the formation of self-assembled fibrillar networks with encapsulated micelles. This prototype system presents an example of orthogonal self-assembly, that is, the independent formation of two different supramolecular structures, each with their own characteristics that coexist within a single system.