How do I convert this ion exchange capacity into water softening capacity?
In the H form there are one plus charged ions ($\ce{H+}$) being exchanged in the water softening process. But the species being exchanged for the $\ce{H+}$ ions are doubly charged ($\ce{Mg^2+}$ and $\ce{Ca^2+}$), so two $\ce{H+}$ ions must be exchanged per $\ce{Mg^2+}$ or $\ce{Ca^2+}$ ion.  

So, "1.0 mEq/mL min of 99% in H form" could equivalently be read as:  

The exchange resin has the ability to exchange $\pu{0.5mmol}$ of $\ce{Mg^2+}$ or $\ce{Ca^2+}$ ions per $\pu{mL}$ of resin.