Energy system models are needed to help policy makers design renewable energy policies that combine support for renewable electricity with support for renewable gas. In this paper, we advance a stylized model that includes demand for electricity, heating, and hydrogen in industry that is supplied by competing technologies. We first show that the status quo in most countries, which is a combination of carbon pricing with support for renewable electricity, only supports green gases indirectly and in a limited way. When we then add direct support for renewable gas to the model, we have two main findings. First, a Renewable Energy Sources - Gas (RES-G) target is more effective in supporting biomethane than in supporting green hydrogen. Second, there are strong interaction effects between a RES-E target and a RES-G target that can be both complementary and substitutive.