Porous graphitic materials containing nitrogen are promising catalysts for photo(electro)chemical reactions, notably water splitting, but can also serve as "molecular sieves". Nitrogen increases the hydrophilicity of the graphite parent material, among other effects. A deeper understanding of how water interacts with C- and N-containing layered materials, if and which differences exist between materials with different N content and pore size, and what the role of water dynamics is - a prerequsite for catalysis and sieving - is largely absent, however. Vibrational spectroscopy can answer some of these questions. In this work, the vibrational dynamics and spectroscopy of deuterated water molecules (D2O) mimicking dense water layers at room temperature on the surfaces of two different C/N-based materials with different N content and pore size, namely graphitic C3N4 (g-C3N4) and C2N, are studied using ab initio molecular dynamics (AIMD). In particular, time-dependent vibrational sum frequency generation (TD-vSFG) spectra of the OD modes and also time-averaged vSFG spectra and OD frequency distributions are computed. This allows us to distinguish "free" (dangling) OD bonds from OD bonds that are bound in a H-bonded water network or at the surface - with subtle differences between the two surfaces and also to a pure water/air interface. It is found that the temporal decay of OD modes is very similar on both surfaces with a correlation time near 4 ps. In contrast, TD-vSFG spectra reveal that the interconversion time from "bonded" to "free" OD bonds is about 8 ps for water on C2N and thus twice as long as for g-C3N4, demonstrating a propensity of the former material to stabilize bonded OD bonds.