Single sheets of hexagonal boron nitride (h-BN) on transition metals provide a model system for layered insulating materials as well as a functional substrate for molecules and metal clusters. The progress in the understanding of h-BN layers on transition metals was mainly driven by scanning tunnelling microscopy (STM) and photoelectron spectroscopy (PES) measurements within the last decade, while direct measurements of mechanical and electrical properties are still rare. Our investigations of the two-dimensional (2D) h-BN nanomesh on a Rh(111) substrate by high-resolution noncontact atomic force microscopy (nc-AFM) reveal a complex surface structure including a frequently observed contrast inversion. Detailed 2D force spectroscopy measurements are revealing towards a mechanical elastic deformation of the h-BN monolayer caused by the tip-sample interaction. Furthermore, Kelvin probe force microscopy (KPFM) and spectroscopy measurements show local work function variations of the nanomesh, proving the results obtained by PES but additionally providing detailed local information.