A novel stable bivariate integer-valued autoregressive moving average (Bivariate IN-ARMA(1,1)) model that takes into account the joint Poisson distribution of the two innovations, is proposed in this study. The conditional maximum likelihood (CML) estimation approach, which is based on the principles of thinning and convolution, is used to estimate the model parameters. Based on certain combinations of the model parameters, a simulation study is carried out to evaluate the effectiveness of the CML technique. An application on COVID-19 data series is also provided.