This study focuses on the modelling of turbulent lifted jet flames using flamelets and presumed PDF approach with interests on both flame lift-off height and flame brush structure. First, flamelet models used to capture contributions from premixed and non-premixed modes to the partially premixed combustion in the lifted jet flame are assessed using a Direct Numerical Simulation (DNS) data for turbulent lifted hydrogen jet flame. The joint PDFs of mixture fraction, Z, and progress variable, c, including their statistical correlation are obtained using a copula method, which is also validated using the DNS data. The statistically independent PDFs are found to be generally inadequate to represent the joint PDFs from the DNS data. The effects of Z-c correlation and contribution from non-premixed combustion mode on the flame lift-off height are studied systematically by including one effect at a time in the simulations used for a posteriori validation. A simple model including the effects of chemical kinetics and scalar dissipation rate is suggested and used for non-premixed combustion contributions. The results clearly show that both Z-c correlation and non-premixed combustion effects are required in the premixed flamelets approach to get a good agreement with the measured flame lift-off heights as function of jet velocity. The flame brush structure reported in earlier experimental studies is also captured reasonably well for various axial positions. It seems that the flame stabilisation is influenced by both premixed and non-premixed combustion modes, and their mutual influences.