In 2020, the European Commission published a hydrogen strategy announcing different policy measures to support the construction of a European hydrogen infrastructure. Hereby, a target of 40 GW installed electrolyser capacity within the EU by 2030 was set, which will cause a significant electricity demand and will link together hydrogen and electricity markets. Therefore, state-of-the-art power modelling must include both electricity and hydrogen. This work proposes a novel approach to integrate hydrogen in existing long-term optimization electricity market dispatch models. A comprehensive modification of the optimization framework is not necessary as the hydrogen market can be modelled in analogy to the electricity market. This is done by implementing hydrogen markets as additional zones within the model with their own hydrogen demands and production. Thus, a hydrogen layer next to the existing electricity layer is created. Next to the dispatch model, hydrogen generation technologies are integrated into a system dynamics investment module, which is interlinked with the optimization model and determines market-driven investments in power plants based on the NPV. As a support scheme for electrolysers, carbon contracts for difference are implemented. Further, a detailed analysis of the German hydrogen and electricity markets is carried out. The analysis shows that renewable energy sources and electrolysers are complementary technologies, which mutually increase their profitability. The model indicates that higher electricity demands caused by electrolysers will not lead to higher electricity prices but reduce the price volatility.