Phonon polaritons are quasiparticles resulting from strong coupling of photons with optical phonons. Excitation and control of these quasiparticles in 2D materials offer the opportunity to confine and transport light at the nanoscale. Here, we image the phonon polariton (PhP) spectral response in thin hexagonal boron nitride (hBN) crystals as a representative 2D material using amplitude- and phase-resolved scattering scanning near-field optical microscopy (s-SNOM) using broadband mid-IR synchrotron radiation. The large spectral bandwidth enables the simultaneous measurement of both out-of-plane (780 cm^-1) and in-plane (1370 cm^-1) hBN phonon modes. In contrast to the strong in-plane mode, the out-of-plane PhP mode response is weak. Measurements of the PhP wavelength reveal a proportional dependence on sample thickness for thin hBN flakes, which can be understood by a general model describing two-dimensional polariton excitation in ultrathin materials.