Terahertz (THz) and sub-THz coherent acoustic phonons have been successfully used as probes of various quantum systems. Since their wavelength is in the nanometer range, they can probe nanostructures buried below a surface with nanometer resolution and enable control of electrical and optical properties on a picosecond time scale. However, coherent acoustic phonons have not yet been widely used to study van der Waals (vdW) two-dimensional (2D) materials and heterostructures. This class of 2D systems features strong covalent bonding of atoms in the layer planes and weak van der Waals attraction between the layers. The dynamical properties of the interface between the layers or between a layer and its supporting substrate are often omitted as they are difficult to probe. On the other hand, these play a crucial role in interpreting experiments and/or designing new device structures. Here, we use picosecond ultrasonic techniques to investigate phonon transport in vdW InSe nanolayers and InSe/hBN heterostructures. Coherent acoustic phonons are generated and detected in these 2D systems and allow us to probe elastic parameters of different layers and their interfaces. In particular, our study of the elastic properties of the interface between vdW layers reveals a strong coupling over a wide range of frequencies up to 0.1 THz, offering prospects for high-frequency electronics and technologies that require control over the charge and phonon transport across an interface. In contrast, we reveal a weak coupling between the InSe nanolayers and sapphire substrates, relevant in thermoelectrics and sensing applications, which can require quasi-suspended layers.