This paper analyzes a mix of alternative policies in supporting the green transition and the phase-out of fossil fuels, without compromising financial stability. An environmental dynamic stochastic general equilibrium (E-DSGE) model with two sectors (green and brown) and endogenous default is developed to assess potential climate-induced financial stability threats that can be mainly generated through physical and transition risks mechanism. Those risks are evaluated through a compound capital depreciation shock and a carbon tax shock. The paper offers several findings. First of all, a too stringent carbon tax would increase the medium-term default rate in both sectors, harming financial stability due to potentially detrimental effects on banks’ balance sheet. Second, there exists a trade-off in implementing green monetary or macroprudential policies: if a policy can encourage the green transition, financial stability is compromised due to a rise in default rates. In contrast, if a policy aims to reduce vulnerabilities and financial stability risks, then the phase-out of the polluting sector to foster the green sector would be hard to achieve. The model finds that under certain physical and transition risks, a dual interest rate policy, coupled with a fiscal policy in which carbon tax revenues are redistributed to households as vouchers to encourage the consumption of green goods, is able to support the green transition and safeguard financial stability. Therefore, top-down and bottom-up approaches are the keys for sustainability in the whole economy and financial system.