The exponential rise in greenhouse gas (GHG) emissions into the environment is one of the major concerns of international organisations and governments. As a result, lowering carbon dioxide (CO2) and methane (CH4) emissions has become a priority across a wide range of industries, including transportation sector, which is recognised as one of the major sources of these emissions. Therefore, renewable energy carriers and powertrain technologies, such as the use of alternative fuels and combustion modes in internal combustion engines, are required. Dual-fuel operation with high substitution ratios using low carbon and more sustainable fuels can be an effective short-term solution. Hythane, a blend of 20% hydrogen and 80% methane, could be a potential solution to this problem. In this research, two alternative diesel-hythane dual-fuel modes, namely conventional dual-fuel (CDF) combustion and reactivity-controlled compression ignition dual-fuel (RCCI DF) combustion, were experimentally evaluated and compared to a conventional diesel combustion (CDC) baseline. The study obtained a high gas substitution fraction (76%) of hythane supplied by a port fuel injection (PFI) system in a 2.0 litre heavy-duty diesel engine at a fixed engine speed of 1200 rpm and 0.6 MPa indicated mean effective pressure (IMEP), a typical part-load operating condition of 25% of total engine load. The results indicate that RCCI DF operation provided the best balance of engine emissions and efficiencies, with a CO2 reduction of up to 40% compared to CDC, and 16% more than CDF, while a 46.6% indicated thermal efficiency (ITE) was achieved, representing 1.7 and 6.9 percentage points higher than CDC and CDF, respectively. Moreover, RCCI DF significantly reduced nitrogen oxides (NOx) formation to 0.46 g/kWh, which resulted in reduced aqueous urea solution consumption. However, taking into account of CH4 emission, RCCI DF operation led to 20% reduction in the overall GHG emissions compared to the CDC baseline, whilst the CDF mode increased GHG formation by 49%.