Triphilic ionic liquids (containing polar, apolar, and fluorinated components) that can hydrogen bond present a new paradigm in ionic liquid structural morphology. In this study we show that butylammonium pentadecafluorooctanoate and its nonfluorinated analogue butylammonium octanoate form disordered bicontinuous phases where a network of charge alternating hydrogen bonds continuously percolate through the whole liquid. These systems show order on multiple length scales, the largest length scale given by the percolating network. Separation between filaments in the network gives rise to a prepeak or first sharp diffraction peak. In the case of the fluorinated system, shorter range order occurs due to apolar-fluorinated alternation that decorates the surface of each individual filament. The backbone of the filaments is the product of the shortest organized length scale, namely, charge alternating hydrogen bonds. Liquid structure obtained via molecular dynamics simulations is used to compute coherent X-ray scattering intensities, and a full picture of the liquid landscape is developed. A careful mathematical analysis of the simulation data proposed here reveals individual molecular correlations that importantly contribute to each feature of the experimental structure function.