Guided-wave characteristics of a new hybrid or composite structure that consists of a non-radiative dielectric (NRD) waveguide surface mounted on the top of a relatively thin dielectric substrate are presented. This proposed structure is thus no longer a conventional NRD guide because its asymmetry may potentially generate unwanted leakage loss. Detailed numerical results show that one of the most interesting features is that it can still preserve a great deal of the desired properties of the conventional NRD guide under certain circumstances. This structure allows for a direct hybrid integration of a planar microstrip circuit with the NRD guide, thus providing an alternative design building block to a class of 3D multilayered millimetre-wave circuits. Experiments further verify the low-loss characteristics of the structure. In addition, effects of the width of ground plane are also discussed to show its low or non-radiating guided wave properties. A basic guideline in the design of a low-loss surface mounted NRD guide is provided.