Phonon polaritons (PPs) in van der Waals (vdW) materials can strongly enhance light-matter interactions at mid-infrared frequencies, owing to their extreme infrared field confinement and long lifetimes. PPs thus bear potential for achieving vibrational strong coupling (VSC) with molecules. Although the onset of VSC has recently been observed spectroscopically with PP nanoresonators, no experiments so far have resolved VSC in real space and with propagating modes in unstructured layers. Here, we demonstrate by real-space nanoimaging that VSC can be achieved between propagating PPs in thin vdW crystals (specifically h-BN) and molecular vibrations in adjacent thin molecular layers. To that end, we performed near-field polariton interferometry, showing that VSC leads to the formation of a propagating hybrid mode with a pronounced anti-crossing region in its dispersion, in which propagation with negative group velocity is found. Numerical calculations predict VSC for nanometer-thin molecular layers and PPs in few-layer vdW materials, which could make propagating PPs a promising platform for ultra-sensitive on-chip spectroscopy and strong coupling experiments.