The advancement of AI-assisted myopia screening necessitates the joint diagnosis of both-eye (OU) high myopia (HM) status and the prediction of axial length (AL). This clinical requirement introduces a complex mixed-type (binary-continuous) multitask learning task with bi-domain (OU) image covariates, giving rise to two key challenges: i) capture the inter-ocular asymmetry of OU images within a cutting-edge foundation model; ii) model and estimate the conditional dependence structure among mixed-type multivariate responses given image covariates. We address the challenges by: i) imposing residual adapters on the Vision Transformer foundation model to capture the OU similarity and heterogeneity simultaneously; ii) developing a four-dimensional copula loss that is implementable in PyTorch based on a latent variable expression for the Gaussian copula likelihood, and proposing a computationally efficient fast Monte Carlo Expectation Maximization (fMCEM) algorithm to estimate copula parameters. We further formulate a specific overfitting problem called stronger covariance phenomenon in multitask learning. We reveal the disturbance of the phenomenon to estimation of copula parameters and theoretically demonstrate the numerical stability of the proposed fMCEM algorithm against the disturbance. The application to our annotated OU ultra-widefield fundus image dataset and simulation on synthetic data demonstrate that our method stably enhances the predictive capabilities on both classification and regression tasks.