When my husband and I try to discuss important issues, we usually wind up arguing, fighting, or shutting down. What can we do?

This is a typical anxiety issue where one is trying to prove a point and win the argument. If it is an important matter to be discussed, both of you need to set aside the ego and focus on the goal of sorting out the problem. Argument is healthy only if you know how to handle criticism, it ends in a fight when either of you do not take the argument in to healthy discussion. One should not take it personally especially when it involves your loved ones.