A new stochastic model for the co-dynamics of SARS-CoV-2 (COVID-19) and Hepatitis B virus (HBV) is presented and rigorously analyzed. The boundary and co-existence of endemic equilibria are presented for the deterministic equivalence of the model. Also, conditions for the existence and uniqueness of a unique global solution are derived for the stochastic version of the model. Using the Lyapunov function, the solution of the stochastic model is shown to fluctuate around the disease-free equilibrium of the deterministic system under a certain scenario. Furthermore, conditions for disease extinction and ergodic stationary distribution are derived for the stochastic model. Numerical simulations are implemented to justify obtained theoretical results. The results show that, for the scenario when the stochastic and deterministic related reproduction numbers are below 1, both diseases and their co-infections die out and go into extinction. However, for the scenario when both reproduction numbers are greater than 1, both diseases and their co-infections co-exist for a long time.