The lattice dynamical properties of dilute InAs1−xNx/InP (001) epilayers (0 ≤ x ≤ 0.03) grown by gas-source molecular beam epitaxy were carefully studied experimentally and theoretically. A high-resolution Brüker IFS 120 v/S spectrometer was employed to measure the room-temperature infrared reflectivity (IRR) spectra at near-normal incidence (θi = 0). The results in the frequency range of 180–500 cm−1 revealed accurate values of the characteristic In-As-like and In-N-like vibrational modes. For InAs1−xNx alloys, a classical “Drude–Lorentz” model was constructed to obtain the dielectric functions ε~ω in the far IR regions by incorporating InAs-like and InN-like transverse optical ωTO modes. Longitudinal optical ωLO phonons were achieved from the imaginary parts of the simulated dielectric loss functions. The theoretical results of IRR spectra for InAs1−xNx/InP (001) epilayers using a multi-layer optics methodology provided a very good agreement with the experimental data. At oblique incidence (θi ≠ 0), our study of s- and p-polarized reflectance (Rs,p(ω)) and transmission (Ts,p(ω)) spectra allowed the simultaneous perception of the ωTO and ωLO phonons of the InAs, InN and InAs0.97N0.03 layers. Based on the average t-matrix Green’s function theory, the results of local vibrational modes for light SiIn+ donors and SiAs−, CAs− acceptors in InAs were found in good agreement with the existing Raman scattering and infrared spectroscopy data. InInN, however, the method predicted an in-band mode for the MgIn− acceptor while projecting an impurity mode of the SiIn+ donor to appear just above the maximum ωmaxInN[≡595 cm−1] phonon frequency region. In InAs1−xNx/InP (001) epifilms, the comparison of reflectivity/transmission spectra with experiments and the predictions of impurity modes for isoelectronic donor and acceptor impurities in InAs and InN can be valuable for appraising the role of defects in other technologically important semiconductors.