Van der Waals (vdW) heterostructures assembled from layers of two-dimensional materials have attracted considerable interest due to their novel optical and electrical properties. Here, we report a scattering-type scanning near-field optical microscopy study of hexagonal boron nitride on black phosphorus (h-BN/BP) heterostructures, demonstrating the first direct observation of in-plane anisotropic phonon polariton modes in vdW heterostructures. Notably, the measured in-plane optical anisotropy along the armchair and zigzag crystal axes exceeds the ratio of refractive indices of BP in the x-y plane. We explain that this enhancement is due to the high confinement of the phonon polaritons in h-BN. We observe a maximum in-plane optical anisotropy of αmax = 1.25 in the frequency spectrum at 1405 to 1440 cm-1. These results provide new insights into the behavior of polaritons in vdW heterostructures, and the observed anisotropy enhancement paves the way to novel nanophotonic devices and to a new way to characterize optical anisotropy in thin films.