The U(1) and U(2) are the shocks and the H are the variances. If you want to define a simple bivariate GARCH-M process from that, you could do something like
set x = 5+.3*h(t)(1,1)+u(1)
set y = 3+.1*h(t)(2,2)+u(2)
The +u(1) and +u(2) are the only parts that a "required" for making this a bivariate GARCH model. The other terms are for the mean model that you want. The matrix h(t) is a 2 x 2 array with the variances in the (1,1) and (2,2) slots and the covariance in (1,2). So x includes the variance of process 1 and y includes the variance of process 2 in the mean.