Thermoelectric devices have potential energy conversion applications ranging from space exploration through to mass-market products. Standardised, accurate and repeatable high-throughput measurement of their properties is a key enabling technology. Impedance spectroscopy has shown promise as a tool to parametrically characterise thermoelectric modules with one simple measurement. However, previously published models which attempt to characterise fundamental properties of a thermoelectric module have been found to rely on heavily simplified assumptions, leaving its validity in question. In this paper a new comprehensive impedance model is mathematically developed. The new model integrates all relevant transport phenomena: thermal convection, radiation, and spreading-constriction at junction interfaces. Additionally, non-adiabatic internal surface boundary conditions are introduced for the first time. These phenomena were found to significantly alter the low and high frequency response of Nyquist spectra, showing their necessity for accurate characterisation. To validate the model, impedance spectra of a commercial thermoelectric module was experimentally measured and parametrically fitted. Technique precision is investigated using a Monte-Carlo residual resampling approach. A complete characterisation of all key thermoelectric properties as a function of temperature is validated with material property data provided by the module manufacturer. Additionally, by firstly characterising the module in vacuum, the ability to characterise a heat transfer coefficient for free and forced convection is demonstrated. The model developed in this study is therefore a critical enabler to potentially allow impedance spectroscopy to characterise and monitor manufacturing and operational defects in practical thermoelectric modules across multiple sectors, as well as promote new sensor technologies.