A tire and wheel rim assembly includes a tire supporting rim having an outward facing mounting surface and at least one tire body mounted to the rim and positioning an internal tire cavity over the rim mounting surface. A tire pressure monitoring module assembly mounts to the rim mounting surface and includes a housing having an internal pressure chamber; a pressure sensing device and/or a temperature measuring sensor within the housing pressure chamber; and an elongate connecting member extending through the housing and the rim mounting surface. The connecting member has an axial through-passageway communicating with the internal tire cavity and the housing pressure chamber. The connecting member may be configured as an externally threaded bolt having an axial through-passageway. The bolt is in threaded engagement with a threaded opening in the housing and extends through the rim outside mounting surface to couple the housing to the rim. The inflation pressure in the tire cavity is transferred through the axial passageway of the threaded bolt to the pressure chamber within the module housing. The tire pressure monitoring module assembly, attached to the rim outward mounting surface, is positioned in a non-contacting relationship with the one or more tire bodies mounted to side of the rim opposite the rim mounting surface.