The silicone oil (SO)-silicone rubber (SiR) biphasic dielectric composite serves as irreplaceable internal insulation structure in fluid-filled cable terminations. Moisture ingress is universally acknowledged as the main factor causing internal insulation degradation and subsequent failure of terminations. However, there is little knowledge on moisture transfer in SO-SiR systems, especially when taking swelling effect into consideration, which restricts deeper understanding of the failure mechanism of the termination insulation. In this work, the moisture transfer characteristics in SO-SiR are investigated by measuring the moisture content of SO and SiR during immersion with different moisture content levels at different temperature levels. When the initial moisture content of SO is below similar to 40 ppm, water transfers from SiR to SO, and the opposite transfer direction occurs at higher moisture levels. The rise of temperature facilitates moisture transfer and results in more moisture content in SO and less in SiR at equilibrium. Moreover, experiments to determine the swelling degree of SO-SiR are performed, and the results and model analysis indicated that the swelling is a Langmuir-type diffusion process. It is found that the time to reach moisture equilibrium lags behind that to reach swelling equilibrium in SO-SiR. On this basis, further analysis concludes the moisture transfer process under the swelling effect into three stages from the beginning of immersion to equilibrium and reveals the mechanism behind it. Finally, moisture equilibrium curves for SO-SiR system are presented.