Being able to sing vocal harmony has more to do with your ears than it has to do with your voice.
You need to train your ears to firstly hear the different harmonies that are available and then to stop yourself from being influenced by the other singer so that you can stick to your melody line.
There is a simple but effective exercise that you can do which will help you to achieve both of these things.
I recommend doing this exercise a couple of times a week for a few weeks in order to start seeing (or should I say hearing) results!
Extra tip: I like to do this with a pot of smarties or MnMs. Once I move 20 smarties from one pot into another because I have answered 20 notes correct in a row… I get to eat them! 🙂
Now THAT’S incentive!!