Can you love the person, but hate the sin?

In light of all the heinous acts committed recently, I wondered how are Christians supposed to respond?  Do we have the ability to separate our love for people/humanity from their behavior/actions?  When we show love, are we expressing approval for their behavior?  Are we letting the person off the hook?  Is this biblical?  Listen as I share my journey of reconciling my feelings and learning how to love people like God loves us; unconditionally.