If you both have it, you both have it, it can't be passed back and forth. As far as actually getting rid of it, you will always have the virus but usually people's immune systems makes it go dormant eventually, and that's the end of it.
As to how fast this works depends on the individual, but the general time given for when it's typically gone is within 2 years. Improving your diet and increasing your anti-oxidant intake could boost you immune system to help speed up the process.