Capacity enhancement by utilising the unused spectral bands of the low-loss optical window of standard singlemode fibre (SSMF) is a cost-effective solution for meeting the future demand for data traffic. The development of optical amplifiers that can operate in different spectral bands is expected to play an integral part in the establishment of multi-band networks. In this work, we perform experimental, analytical and numerical modelling of a multi-band transmission system using a hybrid distributed-discrete Raman amplifier enabling signal amplification from 1410-1605 nm. The developed amplifier was tested over 50km of SSMF using 200 Gbit/s channels, where successful transmission was achieved, well above the HD-FEC threshold of 8.5 dB. Further study on the multi-band transmission performance was carried out using a semi-analytical closed-form approximation and split-step Fourier method-based simulations for various related test cases. The analytical and numerical models are also compared with experimental results, showing reasonable agreement in terms of system performance estimation.